S. Liao

发表

Chaos: a bridge from microscopic uncertainty to macroscopic randomness

S. Liao, 2011, 1108.4472.

A consistent and balanced-force model for incompressible multiphase flows on polyhedral unstructured grids

S. Liao, B. Xie, P. Jin, 2020 .

A new modification of false position method based on homotopy analysis method

S. Abbasbandy, S. Liao, 2008 .

A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method

Shijun Liao, S. Liao, 1992 .

A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics

S. Liao, 1997 .

An explicit, totally analytic approximate solution for Blasius’ viscous flow problems

S. Liao, 1999 .

An analytic approximate approach for free oscillations of self-excited systems

S. Liao, 2004 .

Notes on the homotopy analysis method: Some definitions and theorems

S. Liao, 2009 .

An optimal homotopy-analysis approach for strongly nonlinear differential equations

S. Liao, 2010 .

Foundations of offshore wind turbines: A review

Tongguang Wang, S. Liao, A. Borthwick, 2019, Renewable & Sustainable Energy Reviews.

Application of Homotopy Analysis Method in Nonlinear Oscillations

S. Liao, A. Chwang, 1998 .

A new method for homoclinic solutions of ordinary differential equations

S. Liao, K. Vajravelu, F. Akyildiz, 2009 .

A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate

S. Liao, 1999, Journal of Fluid Mechanics.

AN EXPLICIT TOTALLY ANALYTIC APPROXIMATION OF BLASIUS VISCOUS FLOW PROBLEMS

S. Liao, 1999 .

Beyond Perturbation: Introduction to the Homotopy Analysis Method

S. Liao, S. Sherif, S. Sherif, 2003 .

On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet

S. Liao, 2003, Journal of Fluid Mechanics.

Series solutions of nano boundary layer flows by means of the homotopy analysis method

R. Mohapatra, S. Liao, K. Vajravelu, 2008 .

A new branch of solutions of boundary-layer flows over an impermeable stretched plate

S. Liao, 2005 .

An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate

S. Liao, 2006 .

Flow of a Weakly Conducting Fluid in a Channel Filled with a Darcy–Brinkman–Forchheimer Porous Medium

Tiegang Fang, S. Liao, B. Zhao, 2010 .

Explicit analytic solution for similarity boundary layer equations

I. Pop, S. Liao, 2004 .

Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones

S. Liao, E. Magyari, 2006 .

Series Solutions of Unsteady Boundary‐Layer Flows over a Stretching Flat Plate

S. Liao, 2006 .

S. Liao, N. Kousar, 2011 .

A general approach to get series solution of non-similarity boundary-layer flows

S. Liao, 2009 .

An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude

S. Liao, 2003 .

Homotopy based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls

S. Liao, Jiezhi Wu, Hang Xu, 2010 .

Exact HAM Solutions for the Viscous Rotational Flowfield in Channels with Regressing and Injecting Sidewalls

S. Liao, Hang Xu, J. Majdalani, 2010 .

Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward stagnation point

I. Pop, S. Liao, Hang Xu, 2006 .

Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate

I. Pop, S. Liao, Hang Xu, 2007 .

Homotopy analysis of nonlinear progressive waves in deep water

K. Cheung, S. Liao, 2003 .

Solving solitary waves with discontinuity by means of the homotopy analysis method

S. Liao, Wan Wu, 2005 .

Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium

I. Pop, S. Liao, Jun Cheng, 2005 .

An approximate solution technique not depending on small parameters: A special example

S. Liao, 1995 .

Numerically solving non-linear problems by the homotopy analysis method

S. Liao, 1997 .

Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method

S. Liao, Chun Wang, Yongyan Wu, 2005 .

Series solutions of coupled Van der Pol equation by means of homotopy analysis method

B. T. Nohara, S. Liao, Yajie Li, 2010 .

An analytic approximation of the drag coefficient for the viscous flow past a sphere

S. Liao, 2002 .

On the clean numerical simulation (CNS) of chaotic dynamic systems

S. Liao, 2017 .

Analytic solutions of the temperature distribution in Blasius viscous flow problems

Shijun Liao, Antonio Campo, S. Liao, 2002, Journal of Fluid Mechanics.

On the explicit analytic solution of Cheng-Chang equation

Ioan Pop, Shijun Liao, I. Pop, 2003 .

Dual solutions of boundary layer flow over an upstream moving plate

Shijun Liao, Hang Xu, S. Liao, 2008 .

An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate

Shijun Liao, S. Liao, 1998 .

On model for three-dimensional flow of nanofluid: An application to solar energy

Tasawar Hayat, Shijun Liao, Meraj Mustafa, 2014 .

AN APPROXIMATE SOLUTION TECHNIQUE WHICH DOES NOT DEPEND UPON SMALL PARAMETERS: A SPECIAL EXAMPLE

Shijun Liao, S. Liao, 1995 .

AN APPROXIMATE SOLUTION TECHNIQUE WHICH DOES NOT DEPEND UPON SMALL PARAMETERS (PART 2): AN APPLICATION IN FLUID MECHANICS

Shijun Liao, S. Liao, 1997 .

Collisionless periodic orbits in the free-fall three-body problem

S. Liao, Xiaoming Li, 2018, New Astronomy.

Over a thousand new periodic orbits of a planar three-body system with unequal masses

Y. Jing, S. Liao, Xiaoming Li, 2018 .

On the limiting Stokes wave of extreme height in arbitrary water depth

S. Liao, Xiaoxu Zhong, 2017, Journal of Fluid Mechanics.

The effect of numerical noises on statistics of a chaotic dynamical system

S. Liao, Xiaochen Li, Xiaoming Li, 2018, Journal of Physics: Conference Series.

The influence of numerical noises on statistics computation of chaotic dynamic systems

S. Liao, Xiaoming Li, 2016, 1609.09354.

On the reliable long-term simulation of chaos of Lorenz equation in the interval [0,10000]

Shijun Liao, S. Liao, Peifeng Wang, 2013 .

A comment on the arguments about the reliability and convergence of chaotic simulations

S. Liao, 2014, 1401.0256.

Steady-state resonance of multiple wave interactions in deep water

S. Liao, Zeng-Xing Liu, 2014, Journal of Fluid Mechanics.

Analytic solutions of the rise dynamics of liquid in a vertical cylindrical capillary

Bohua Sun, S. Liao, Xiaoxu Zhong, 2018, European Journal of Mechanics - B/Fluids.

Systematic Descriptions and Related Theorems

S. Liao, 2012 .

Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations

S. Liao, Qiang Yu, Hang Xu, 2018, Applied Mathematical Modelling.

Series Solution of Non-similarity Boundary-Layer Flows Over a Porous Wedge

S. Liao, N. Kousar, 2010 .

On the Discovery of the Steady-State Resonant Water Waves

S. Liao, Zeng-Xing Liu, Da-li Xu, 2016 .

Equilibrium states of class-I Bragg resonant wave system

S. Liao, Zhiliang Lin, Da-li Xu, 2015 .

A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows

S. Liao, Hang Xu, 2007 .

Series solutions of unsteady MHD flows above a rotating disk

S. Liao, Hang Xu, 2006 .

Analytic Solutions of Von Kármán Plate under Arbitrary Uniform Pressure — Equations in Differential Form

S. Liao, X. Zhong, 2016, 1604.06708.

An explicit analytic solution for non-Darcy natural convection over horizontal plate with surface mass flux and thermal dispersion effects

S. Liao, Chun Wang, J. M. Zhu, 2003 .

Mathematica Package BVPh

S. Liao, 2012 .

An explicit series approximation to the optimal exercise boundary of American put options

Song‐Ping Zhu, S. Liao, Jun Cheng, 2010 .

SERIES SOLUTION OF LARGE DEFORMATION OF A BEAM WITH ARBITRARY VARIABLE CROSS SECTION UNDER AN AXIAL LOAD

S. Liao, 2009, The ANZIAM Journal.

Analysis of mixed convection flow in an inclined lid-driven enclosure with Buongiorno’s nanofluid model

S. Liao, Qiang Yu, Hang Xu, 2018, International Journal of Heat and Mass Transfer.

Three-body problem — From Newton to supercomputer plus machine learning

S. Liao, Xiaoming Li, Yu Yang, 2021, New Astronomy.

On the reliability of computed chaotic solutions of non-linear differential equations

S. Liao, 2008, 0901.2986.

A kind of linearity-invariance under homotopy and some simple applications o fit in mechanics

S. Liao, 1992 .

Chapter 1: Chance and Challenge: A Brief Review of Homotopy Analysis Method

S. Liao, 2014 .

Nonlinear Analysis: Real World Applications

S. Liao, N. Kousar, 2010 .

Optimal Homotopy Analysis Method

S. Liao, 2012 .

Solving high Reynolds‐number viscous flows by the general BEM and domain decomposition method

S. Liao, Yongyan Wu, 2005 .

On parallel computing for the general boundary element method

S. Liao, X. Y. Zhao, 2002 .

General boundary element method for Poisson equation with spatially varying conductivity

Shijun Liao, S. Liao, 1998 .

A new branch of the temperature distribution of boundary-layer flows over an impermeable stretching plate

S. Liao, Yue Tan, Hang Xu, 2008 .

On time independent Schrödinger equations in quantum mechanics by the homotopy analysis method

S. Liao, J. Rana, 2019, Theoretical and Applied Mechanics Letters.

Analytic approximations of Von Kármán plate under arbitrary uniform pressure—equations in integral form

S. Liao, Xiaoxu Zhong, 2016, 1604.06711.

Chapter 9: HAM-Based Mathematica Package BVPh 2.0 for Nonlinear Boundary Value Problems

S. Liao, Yinlong Zhao, 2014 .

A Modified Homotopy Analysis Method for Solving Boundary Layer Equations

S. Liao, Zhiliang Lin, Yinlong Zhao, 2013 .

Relationship to Euler Transform

S. Liao, 2012 .

Unsteady Boundary-layer Flows

S. Liao, 2012 .

Interaction of Nonlinear Water Wave and Nonuniform Currents

S. Liao, 2012 .

A Boundary-layer Flow with an Infinite Number of Solutions

S. Liao, 2012 .

Resonance of Arbitrary Number of Periodic Traveling Water Waves

S. Liao, 2012 .

Nonlinear Boundary-value Problems with Multiple Solutions

S. Liao, 2012 .

EXPLICIT SERIES SOLUTION OF A CLOSURE MODEL FOR THE VON KÁRMÁN–HOWARTH EQUATION

S. Liao, M. Oberlack, Zeng-Xing Liu, 2011 .

Phase velocity effects of the wave interaction with exponentially sheared current

S. Liao, Zeng-Xing Liu, Zhiliang Lin, 2014 .

2022 Avoiding small denominator problems by completely abandoning perturbation methods

S. Liao, 2022 .

Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence

S. Liao, Shijie Qin, 2022, Journal of Fluid Mechanics.

On the free surface motion with a vertical vortex sheet under water

S. Liao, Jing Li, 2018, Journal of Physics: Conference Series.

A general numerical method for solution of gravity wave problems. Part 2: Steady nonlinear gravity waves

S. Liao, 1992 .

A HAM-based analytic approach for physical models with an infinite number of singularities

Ahmed Alsaedi, Shijun Liao, Jifeng Cui, 2015, Numerical Algorithms.

On the general boundary element method

S. Liao, 1998 .

Periodic satellite orbits of the Broucke-Hadjidemetriou-Hénon family of three-body system with unequal masses

S. Liao, Xiaoming Li, 2020 .

Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach

S. Liao, Qiang Yu, Hang Xu, 2018, Numerical Algorithms.

Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems

S. Liao, Xiaoming Li, 2018, Applied Mathematics and Mechanics.

Chaotic motion of three-body problem : an origin of macroscopic randomness of the universe

S. Liao, 2013, 1304.2089.

A new analytic algorithm of Lane-Emden type equations

Shijun Liao, S. Liao, 2003, Appl. Math. Comput..

Higher‐order streamfunction‐vorticity formulation of 2D steady‐state Navier‐Stokes equations

Shijun Liao, S. Liao, 1992 .

A novel homotopy-wavelet approach for solving stream function-vorticity formulation of Navier-Stokes equations

Zhaochen Yang, Shijun Liao, Qiang Yu, 2019, Commun. Nonlinear Sci. Numer. Simul..

Boundary element method for general nonlinear differential operators

Shijun Liao, S. Liao, 1997 .

HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS. PART 2: SOME 2D EXAMPLES

S. Liao, 1997 .

HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS

S. Liao, 1996 .

What's the common ground of all numerical and analytical techniques for nonlinear problems?

S. Liao, 1996 .

GENERAL BOUNDARY ELEMENT METHOD FOR NON‐LINEAR PROBLEMS

S. Liao, A. Chwang, 1996 .

A GENERAL NUMERICAL METHOD FOR THE SOLUTION OF GRAVITY WAVE PROBLEMS. PART 1: 2D STEEP GRAVITY WAVES IN SHALLOW WATER

S. Liao, 1991 .

Some notes on the general boundary element method for highly nonlinear problems

S. Liao, X. Y. Zhao, Y. Wu, 2005 .

A non‐iterative numerical approach for two‐dimensional viscous flow problems governed by the Falker–Skan equation

Shijun Liao, S. Liao, 2001 .

The general boundary element method and its further generalizations

S. Liao, 1999 .

A kind of direct, implicit numerical scheme for unsteady nonlinear problems☆

S. Liao, 1997 .

Homotopy analysis method: A new analytical technique for nonlinear problems

Shijun Liao, S. Liao, 1997 .

On the risks of using double precision in numerical simulations of spatio-temporal chaos

S. Liao, T. Hu, 2019, J. Comput. Phys..

Comparison between Symplectic Integrators and Clean Numerical Simulation for Chaotic Hamiltonian Systems

Shijun Liao, Xiaoming Li, S. Liao, 2016, 1609.09344.

More than six hundred new families of Newtonian periodic planar collisionless three-body orbits

Shijun Liao, Xiaoming Li, S. Liao, 2017, 1705.00527.

A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids

Hiroki Nakayama, Peng Jin, Feng Xiao, 2020, J. Comput. Phys..

SERIES SOLUTIONS OF NON-LINEAR RICCATI DIFFERENTIAL EQUATIONS WITH FRACTIONAL ORDER

Shijun Liao, Hang Xu, S. Liao, 2009 .

On the homotopy analysis method for nonlinear problems

Shijun Liao, S. Liao, 2004, Appl. Math. Comput..

Analysis of nonlinear fractional partial differential equations with the homotopy analysis method

Shijun Liao, Xiangcheng You, Hang Xu, 2009 .

Newton-homotopy analysis method for nonlinear equations

Saeid Abbasbandy, Y. Tan, Shijun Liao, 2007, Appl. Math. Comput..

An analytic approach to solve multiple solutions of a strongly nonlinear problem

Shijun Liao, Shuicai Li, S. Liao, 2005, Appl. Math. Comput..

A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations

S. Liao, Shi-Jun Liao, 1999 .

A HAM-based wavelet approach for nonlinear ordinary differential equations

Zhaochen Yang, Shijun Liao, S. Liao, 2017, Commun. Nonlinear Sci. Numer. Simul..

Explicit series solution of travelling waves with a front of Fisher equation

S. Liao, Yue Tan, Hang Xu, 2007 .

The scaled boundary FEM for nonlinear problems

Shijun Liao, Zhiliang Lin, S. Liao, 2011 .

High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow

Bin Xie, Xi Deng, Shijun Liao, 2019 .

A multigrid approach for steady state laminar viscous flows

S. Liao, F. Mashayek, 2001 .

Commun Nonlinear Sci Numer Simulat

Shijun Liao, S. Liao, 2013 .

Comparison between the homotopy analysis method and homotopy perturbation method

Shijun Liao, S. Liao, 2005, Appl. Math. Comput..

Advances in the homotopy analysis method

Shijun Liao, S. Liao, 2014 .

Homotopy Analysis Method in Nonlinear Differential Equations

Shijun Liao, S. Liao, 2012 .

An explicit solution of the large deformation of a cantilever beam under point load at the free tip

Shijun Liao, Ji Wang, Ji Wang, 2008 .

NUMERICAL SIMULATIONS OF PARTICLE-LADEN AXISYMMETRIC TURBULENT FLOWS

Shijun Liao, S. Liao, F. M Ashayek, 2001 .

Series solutions of unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface

Ioan Pop, Shijun Liao, Hang Xu, 2006 .

A new branch of solutions of boundary-layer flows over a permeable stretching plate

Shijun Liao, S. Liao, 2007 .

Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet

Hang Xu, Shijun Liao, S. Liao, 2009, Comput. Math. Appl..

Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method

Shijun Liao, S. Liao, 2009 .

Series Solution of Three-Dimensional Unsteady Laminar Viscous Flow Due to a Stretching Surface in a Rotating Fluid

Shijun Liao, S. Liao, Yue Tan, 2007 .

Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate

Shijun Liao, Hang Xu, S. Liao, 2005 .

Non-similarity Boundary-layer Flows

S. Liao, 2012 .

Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface

Shijun Liao, S. Liao, N. Kousar, 2010 .

Series solutions of unsteady free convection flow in the stagnation-point region of a three-dimensional body

I. Pop, S. Liao, Hang Xu, 2008 .

A challenging nonlinear problem for numerical techniques

Shijun Liao, S. Liao, 2005 .

Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux

Tasawar Hayat, Shijun Liao, Taseer Muhammad, 2016 .

Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner–Skan flow of nano-fluid

Tasawar Hayat, Shijun Liao, Umar Farooq, 2015 .

Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces

T. Hayat, A. Alsaedi, S. Liao, 2014, Numerical Algorithms.

Unsteady mixed nano-bioconvection flow in a horizontal channel with its upper plate expanding or contracting

Shijun Liao, Ammarah Raees, Hang Xu, 2015 .

Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel

Ahmed Alsaedi, Tasawar Hayat, Shijun Liao, 2014, Appl. Math. Comput..

The explicit series solution of SIR and SIS epidemic models

Ram N. Mohapatra, Hina Khan, K. Vajravelu, 2009, Appl. Math. Comput..

Three-body problem - from Newton to supercomputer plus machine learning pdf

Shijun Liao, Xiaoming Li, Yu Yang, 2021, New Astronomy.

Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method

S. Liao, 2022, Advances in Applied Mathematics and Mechanics.

On the method of directly defining inverse mapping for nonlinear differential equations

Shijun Liao, Yinlong Zhao, S. Liao, 2015, Numerical Algorithms.

Accurate predictions of chaotic motion of a free fall disk

S. Liao, Jing Li, Tianzhuang Xu, 2021, 2102.10386.

Nonlinear Eigenvalue Equations with Varying Coefficients

S. Liao, 2012 .

Steady-state multiple near resonances of periodic interfacial waves with rigid boundary

S. Liao, A. Borthwick, Zeng-Xing Liu, 2020, Physics of Fluids.

A buoyancy vertical transport system of deep-sea mining

S. Liao, 2020 .

On the viscous flow past a sphere: A simplified description

S. Liao, 1999 .

Solution of MHD Flow of Fluid and Heat Transfer Problem via Optimal Homotopy Asymptotic Method

D. Ganji, I. Hashim, S. Liao, 2017 .

A maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations

Zhibin Li, Yinping Liu, Shijun Liao, 2012, J. Syst. Sci. Complex..

A maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations

S. Liao, Zhi-bin Li, Yinping Liu, 2012, Journal of Systems Science and Complexity.

Two and Three Dimensional Gelfand Equation

S. Liao, 2012 .

Some Methods Based on the HAM

S. Liao, 2012 .

On the relationship between the homotopy analysis method and Euler transform

Shijun Liao, S. Liao, 2010 .

Shijun Liao, Xiangcheng You, Hang Xu, 2010 .

Series solutions of stagnation slip flow and heat transfer by the homotopy analysis method

S. Liao, K. Vajravelu, Jun Cheng, 2009 .

Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body

Allen T. Chwang, Shijun Liao, Jian Su, 2006 .

Finding multiple solutions of nonlinear problems by means of the homotopy analysis method

S. Liao, 2006 .

On the explicit, purely analytic solution of Von Kármán swirling viscous flow

Shijun Liao, Cheng Yang, S. Liao, 2006 .

On the steady-state nearly resonant waves

S. Liao, M. Stiassnie, Da-li Xu, 2016, Journal of Fluid Mechanics.

On the existence of steady-state resonant waves in experiments

A. Alsaedi, S. Liao, T. Peng, 2014, Journal of Fluid Mechanics.

On the steady-state fully resonant progressive waves in water of finite depth

Shijun Liao, Zhiliang Lin, Dali Xu, 2012, Journal of Fluid Mechanics.

General boundary element method for non-linear heat transfer problems governed by hyperbolic heat conduction equation

S. Liao, 1997 .

High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow

Feng Xiao, Xi Deng, Shijun Liao, 2019, J. Comput. Phys..

Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method

Feng Xiao, Bin Xie, Xi Deng, 2021, J. Comput. Phys..

Finite amplitude steady-state wave groups with multiple near resonances in deep water

S. Liao, Z. Liu, D. Xu, 2017, Journal of Fluid Mechanics.

Steady-state harmonic resonance of periodic interfacial waves with free-surface boundary conditions based on the homotopy analysis method

S. Liao, A. Borthwick, Zeng-Xing Liu, 2021, Journal of Fluid Mechanics.

Mass, momentum, and energy flux conservation between linear and nonlinear steady-state wave groups

S. Liao, Zeng-Xing Liu, Da-li Xu, 2017 .

On the generalized wavelet-Galerkin method

Zhaochen Yang, Shijun Liao, S. Liao, 2016, J. Comput. Appl. Math..

An explicit solution for the combined heat and mass transfer by natural convection from a vertical wall in a non-Darcy porous medium

Shijun Liao, S. Liao, Chun Wang, 2003 .

On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0,10000]

S. Liao, Pengfei Wang, ShiJun Liao, 2013, 1305.4222.

Faraday waves in a Hele-Shaw cell

S. Liao, B. Xie, Xiaochen Li, 2018 .

A family of new solutions on the wall jet

Shijun Liao, Hang Xu, Guo-Xiong Wu, 2008 .

A short review on the homotopy analysis method in fluid mechanics

Shijun Liao, S. Liao, 2010 .

Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally

S. Liao, Xiaochen Li, Xiaoming Li, 2016, 1608.08894.

One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems

S. Liao, Xiaochen Li, Xiaoming Li, 2020, Science China Physics, Mechanics & Astronomy.

The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum

Y. Jing, S. Liao, Xiaoming Li, 2017, 1709.04775.

On the origin of intrinsic randomness of Rayleigh-Bénard turbulence

Shijun Liao, Lipo Wang, Zhiliang Lin, 2016, Science China Physics, Mechanics & Astronomy.

On the dynamics of the gravitational lifting system in the deep sea mining industry

S. Liao, Jing Li, 2021 .

Stability and hysteresis of Faraday waves in Hele-Shaw cells

S. Liao, Xiaochen Li, Jing Li, 2019, Journal of Fluid Mechanics.

Effect of width on the properties of Faraday waves in Hele-Shaw cells

S. Liao, Chaohe Chen, Xiaochen Li, 2019, Science China Physics, Mechanics & Astronomy.

An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain

Shijun Liao, Zhiliang Lin, Yinlong Zhao, 2013, Comput. Phys. Commun..

On the interaction of deep water waves and exponential shear currents

S. Liao, Jun Cheng, J. Cang, 2009 .

Can machine learning really solve the three-body problem?

S. Liao, Xiaoming Li, Jing Li, 2020 .

On the stability of the three classes of Newtonian three-body planar periodic orbits

Shijun Liao, Xiaoming Li, S. Liao, 2014 .

On the stability of the three classes of Newtonian three-body planar periodic orbits

S. Liao, Xiaoming Li, 2014, Science China Physics, Mechanics & Astronomy.

Influence of numerical noises on computer-generated simulation of spatio-temporal chaos

Shijie Qin, Shijun Liao, S. Liao, 2020 .

On the Inherent Self-Excited Macroscopic Randomness of Chaotic Three-Body Systems

Xiaoming Li, Shijun Liao, S. Liao, 2014, Int. J. Bifurc. Chaos.

Physical limit of prediction for chaotic motion of three-body problem

Shijun Liao, S. Liao, 2013, Commun. Nonlinear Sci. Numer. Simul..

On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems

S. Liao, S. J. Liao, 2011, 1109.0130.

On the reliability of computed chaotic solutions of non-linear differential equations

Shijun Liao, S. Liao, 2008, 0901.2986.

On the periodic solutions of the three-body problem

S. Liao, Xiaoming Li, 2019, National science review.

General boundary element method: an application of homotopy analysis method☆

Shijun Liao, S. Liao, 1998 .

Finite-amplitude steady-state resonant waves in a circular basin

F. Dias, S. Liao, Zeng-Xing Liu, 2021, Journal of Fluid Mechanics.

Three-body problem - from Newton to supercomputer plus machine learning

S. Liao, Xiaoming Li, Yu Yang, 2021, New Astronomy.

On the general Taylor theorem and its applications in solving non-linear problems

S. Liao, 1997 .

Over a thousand new periodic orbits of a planar three-body system with unequal masses

Y. Jing, S. Liao, Xiaoming Li, 2017, 1709.04775.

Foundations of offshore wind turbines: A review

Tongguang Wang, S. Liao, A. Borthwick, 2019, Renewable and Sustainable Energy Reviews.