A time-splitting Galerkin finite element method for the Davey-Stewartson equations

Abstract In this paper, we propose a time-splitting Galerkin method to investigate the evolution of the Davey–Stewartson equations. Using time-splitting, we split the nonlinear equations into two subequations: a linear equation and a nonlinear equation. The nonlinear equation is directly solved and the linear equation is approximated by Galerkin finite element. The error norms and conservation variables of four numerical experiments illustrate the efficiency and accuracy of our numerical scheme.

[1]  C. Klein,et al.  Numerical Study of Blowup in the Davey-Stewartson System , 2011, 1112.4043.

[2]  Anjan Biswas,et al.  Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity , 2011 .

[3]  L. Redekopp,et al.  On two-dimensional packets of capillary-gravity waves , 1977, Journal of Fluid Mechanics.

[4]  K. Stewartson,et al.  On three-dimensional packets of surface waves , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Jaime Angulo Pava,et al.  Nonlinear Dispersive Equations , 2009 .

[6]  Jean-Michel Ghidaglia,et al.  On the initial value problem for the Davey-Stewartson systems , 1990 .

[7]  Li Shan,et al.  Partitioned Time Stepping Method for Fully Evolutionary Stokes-Darcy Flow with Beavers-Joseph Interface Conditions , 2013, SIAM J. Numer. Anal..

[8]  O. H. El-Kalaawy,et al.  Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas , 2012 .

[9]  Rémi Carles,et al.  Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations , 2009, SIAM J. Math. Anal..

[10]  G. Ponce,et al.  Introduction to Nonlinear Dispersive Equations , 2009 .

[11]  Boris A. Malomed,et al.  Solitons in nonlinear lattices , 2011 .

[12]  Andrew G. Glen,et al.  APPL , 2001 .

[13]  Liquan Mei,et al.  Numerical solutions of RLW equation using Galerkin method with extrapolation techniques , 2012, Comput. Phys. Commun..

[14]  C. Babaoglu.  Long-wave short-wave resonance case for a generalized Davey–Stewartson system , 2008 .

[15]  B. M. Fulk.  MATH , 1992 .

[16]  Jaime Angulo Pava,et al.  Solitary and periodic travelling wave solutions , 2009 .

[17]  C. Klein,et al.  Fourth Order Time-Stepping for Kadomtsev-Petviashvili and Davey-Stewartson Equations , 2011, SIAM Journal on Scientific Computing.

[18]  M. Ablowitz,et al.  Nonlinear Evolution Equations-Two and Three Dimensions , 1975 .

[19]  N. Mauser,et al.  Numerical study of the Davey-Stewartson system , 2004 .

[20]  V. Arkadiev,et al.  Inverse scattering transform method and soliton solutions for davey-stewartson II equation , 1989 .

[21]  C. Klein,et al.  Numerical study of the semiclassical limit of the Davey–Stewartson II equations , 2014, 1401.4745.

[22]  Yasuhiro Ohta,et al.  Dynamics of rogue waves in the Davey–Stewartson II equation , 2012, 1212.0152.

[23]  Gulcin M. Muslu,et al.  Numerical simulation of blow-up solutions for the generalized Davey–Stewartson system , 2011, Int. J. Comput. Math..

[24]  Anjan Biswas,et al.  The G'/G method and 1-soliton solution of the Davey-Stewartson equation , 2011, Math. Comput. Model..

[25]  Jibin Li,et al.  Analytical travelling wave solutions and parameter analysis for the (2+1)-dimensional Davey–Stewartson-type equations , 2013 .

[26]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[27]  Hossein Jafari,et al.  The first integral method and traveling wave solutions to Davey–Stewartson equation , 2012 .