Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.

[1]  Guo Boling,et al.  Ill-Posedness for the Nonlinear Davey-Stewartson Equation , 2008 .

[2]  Ji-Huan He,et al.  Variational iteration method for delay differential equations , 1997 .

[3]  F. Austin,et al.  THE VARIATIONAL ITERATION METHOD WHICH SHOULD BE FOLLOWED , 2010 .

[4]  G. Pang.  Conservation laws of the quantized Davey-Stewartson II system , 1993 .

[5]  Ji-Huan He.  Variational iteration method—Some recent results and new interpretations , 2007 .

[6]  Gulcin M. Muslu,et al.  Closing the gap in the purely elliptic generalized Davey-Stewartson system , 2008 .

[7]  E. V. Krishnan,et al.  Exact solutions to the combined KdV–mKdV equation by the extended mapping method , 2006 .

[8]  Khaled Omrani,et al.  The use of variational iteration method and homotopy perturbation method for solving two nonlinear equations , 2011 .

[9]  M. Labidi,et al.  Numerical simulation of the modified regularized long wave equation by He's variational iteration method , 2011 .

[10]  Propagating wave patterns and ''peakons'' of the Davey-Stewartson system , 2006 .

[11]  H. Jafari,et al.  Numerical Solution of the Davey-Stewartson Equations using Variational Iteration Method , 2010 .

[12]  34 - Modeling the Davey-Stewartson (DS) Equations , 2010 .

[13]  Mehdi Dehghan,et al.  Improvement of He's variational iteration method for solving systems of differential equations , 2009, Comput. Math. Appl..

[14]  Abdul-Majid Wazwaz,et al.  The variational iteration method for solving linear and nonlinear systems of PDEs , 2007, Comput. Math. Appl..

[15]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[16]  C. Rogers,et al.  Propagating wave patterns for the 'resonant' Davey-Stewartson system , 2009 .

[17]  Yuzhao Wang,et al.  The Cauchy problem for the elliptic–hyperbolic Davey–Stewartson system in Sobolev space , 2010 .

[18]  Zhenya Yan,et al.  Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey–Stewartson-type equation via a new method , 2003 .

[19]  C. Babaoglu.  Some special solutions of a generalized Davey–Stewartson system , 2006 .

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

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

[22]  M. Jaulent,et al.  Fermionic analysis of Davey-Stewartson dromions☆ , 1990 .

[23]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[24]  Anjan Biswas,et al.  Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods , 2010 .