Method for constructing analytical solutions to the Dym initial value problem
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[1] S. Liao. Notes on the homotopy analysis method: Some definitions and theorems , 2009 .
[2] S. Liao. An explicit, totally analytic approximate solution for Blasius’ viscous flow problems , 1999 .
[3] Robert A. Van Gorder,et al. Nano boundary layers over stretching surfaces , 2010 .
[4] Robert A. Van Gorder,et al. Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation , 2013, Numerical Algorithms.
[5] D. P. Novikov,et al. Algebraic-geometric solutions of the Harry Dym equation , 1999 .
[6] D. J. Kaup,et al. Squared eigenfunctions and the perturbation theory for the nondegenerate N × N operator: a general outline , 2010 .
[7] Ram N. Mohapatra,et al. Implicit differential equation arising in the steady flow of a Sisko fluid , 2009, Appl. Math. Comput..
[8] S. Liao,et al. Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .
[9] A. Bataineh,et al. The comparison between Homotopy Analysis Method and Optimal Homotopy Asymptotic Method for nonlinear age-structured population models , 2012 .
[10] Kadanoff,et al. Exact solutions for the Saffman-Taylor problem with surface tension. , 1990, Physical review letters.
[11] S. Liao,et al. Solving solitary waves with discontinuity by means of the homotopy analysis method , 2005 .
[12] L. A. Dmitrieva,et al. The higher-times approach to multisoliton solutions of the Harry Dym equation , 1993 .
[13] Mustafa Turkyilmazoglu,et al. Purely analytic solutions of the compressible boundary layer flow due to a porous rotating disk with heat transfer , 2009 .
[14] S. Liao. AN EXPLICIT TOTALLY ANALYTIC APPROXIMATION OF BLASIUS VISCOUS FLOW PROBLEMS , 1999 .
[15] Shijun Liao,et al. On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..
[16] Robert A. Van Gorder,et al. Control of error in the homotopy analysis of semi-linear elliptic boundary value problems , 2012, Numerical Algorithms.
[17] S. Liao,et al. Homotopy based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls , 2010 .
[18] Shijun Liao,et al. Analytic solutions of the temperature distribution in Blasius viscous flow problems , 2002, Journal of Fluid Mechanics.
[19] S. Liao. An optimal homotopy-analysis approach for strongly nonlinear differential equations , 2010 .
[20] Robert A. Van Gorder,et al. Analytic and numerical solutions to the Lane–Emden equation , 2008 .
[21] T. Hayat,et al. On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder , 2007 .
[22] Robert A. Van Gorder,et al. Analytical method for the construction of solutions to the Föppl-von Kármán equations governing deflections of a thin flat plate , 2012 .
[23] Shijun Liao,et al. Homotopy Analysis Method in Nonlinear Differential Equations , 2012 .
[24] Robert A. Van Gorder,et al. The inverse scattering transform and squared eigenfunctions for the nondegenerate 3 × 3 operator and its soliton structure , 2010 .
[25] Robert A. Van Gorder,et al. Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer , 2013 .
[26] Fritz Gesztesy,et al. Isospectral deformations for Strum-Liouville and Dirac-type operators and associated nonlinear evolution equations , 1992 .
[27] S. Liao. A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate , 1999, Journal of Fluid Mechanics.
[28] M Turkyilmazoglu. An effective approach for approximate analytical solutions of the damped Duffing equation , 2012 .
[29] K. Vajravelu,et al. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach , 2009 .
[30] Reza Mokhtari,et al. Exact Solutions of the Harry?Dym Equation , 2011 .
[31] S. Liao,et al. Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method , 2005 .
[32] Mohd. Salmi Md. Noorani,et al. Solutions of time-dependent Emden–Fowler type equations by homotopy analysis method , 2007 .
[33] R. Mohapatra,et al. Series solutions of nano boundary layer flows by means of the homotopy analysis method , 2008 .
[34] Colin Rogers,et al. The Harry Dym equation in 2+1 dimensions: A reciprocal link with the Kadomtsev-Petviashvili equation , 1987 .
[35] Saeid Abbasbandy,et al. Mathematical properties of ℏ-curve in the frame work of the homotopy analysis method , 2011 .
[36] Shijun Liao,et al. On the steady-state fully resonant progressive waves in water of finite depth , 2012, Journal of Fluid Mechanics.
[37] Robert A. Van Gorder,et al. Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation , 2013, Numerical Algorithms.
[38] Allen T. Chwang,et al. Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body , 2006 .
[39] M. Kruskal,et al. Nonlinear wave equations , 1975 .
[40] S. Abbasbandy. Homotopy analysis method for heat radiation equations , 2007 .
[41] Robert A. Van Gorder,et al. Gaussian waves in the Fitzhugh–Nagumo equation demonstrate one role of the auxiliary function H(x, t) in the homotopy analysis method , 2012 .
[42] S. Abbasbandy. THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER , 2006 .
[43] S. Abbasbandy,et al. Soliton solutions for the fifth-order KdV equation with the homotopy analysis method , 2007 .
[44] Robert A. Van Gorder,et al. Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6 , 2010, Appl. Math. Comput..
[45] First-order soliton perturbation theory for a generalized KdV model with stochastic forcing and damping , 2011 .
[46] Shijun Liao,et al. A new analytic algorithm of Lane-Emden type equations , 2003, Appl. Math. Comput..
[47] Mustafa Turkyilmazoglu,et al. Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere , 2011 .
[48] S. Liao. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet , 2003, Journal of Fluid Mechanics.
[49] T. Hayat,et al. Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt , 2007 .
[50] Y. Tan,et al. A General Approach to Obtain Series Solutions of Nonlinear Differential Equations , 2007 .
[51] Mohd. Salmi Md. Noorani,et al. Homotopy analysis method for singular IVPs of Emden–Fowler type , 2009 .
[52] M Turkyilmazoglu. The Airy equation and its alternative analytic solution , 2012 .
[53] M. Turkyilmazoglu,et al. Solution of the Thomas–Fermi equation with a convergent approach , 2012 .
[54] Willy Hereman,et al. Derivation and implicit solution of the Harry Dym equation and its connections with the Korteweg-de Vries equation , 1989 .