The Modified Extended Direct Algebraic Method for Solving Nonlinear Partial Differential Equations

By means of modified extended direct algebraic (MEDA) method the multiple ex- act complex solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. New complex solutions for non- linear equations such as one-dimensional Burgers, KDV-Burgers, coupled Burgers and two- dimensional Burgers' equations are obtained.

[1]  A. Ali.  The modified extended tanh-function method for solving coupled MKdV and coupled Hirota–Satsuma coupled KdV equations , 2007 .

[2]  A. A. Soliman,et al.  Modified extended tanh-function method and its application on nonlinear physical equations , 2006 .

[3]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

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

[5]  A. Soliman.  On the solution of two-dimensional coupled Burgers’ equations by variational iteration method , 2009 .

[6]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[7]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .

[8]  A. A. Soliman,et al.  Numerical simulation of the generalized regularized long wave equation by He's variational iteration method , 2005, Math. Comput. Simul..

[9]  Mingliang Wang.  Exact solutions for a compound KdV-Burgers equation , 1996 .

[10]  A. A. Soliman,et al.  Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations , 2007 .

[11]  A. A. Soliman,et al.  New Exact Solutions of Some Nonlinear Partial Differential Equations , 2008 .

[12]  S. A. El-Wakil,et al.  Modified extended tanh-function method and its applications to nonlinear equations , 2005, Appl. Math. Comput..

[13]  Clive A. J. Fletcher,et al.  A comparison of finite element and finite difference solutions of the one- and two-dimensional Burgers' equations , 1983 .

[14]  A. A. Soliman,et al.  New application of Exp-function method for improved Boussinesq equation , 2007 .

[15]  A. A. Soliman,et al.  A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations , 2006 .

[16]  Chuntao Yan.  A simple transformation for nonlinear waves , 1996 .

[17]  A. A. Soliman,et al.  The numerical simulation for stiff systems of ordinary differential equations , 2007, Comput. Math. Appl..

[18]  Fred Wubs,et al.  An explicit-implicit method for a class of time-dependent partial differential equations , 1992 .

[19]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[20]  S. Radwan.  Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation , 2005 .

[21]  Mingliang Wang.  SOLITARY WAVE SOLUTIONS FOR VARIANT BOUSSINESQ EQUATIONS , 1995 .

[22]  A. Refik Bahadir,et al.  A fully implicit finite-difference scheme for two-dimensional Burgers' equations , 2003, Appl. Math. Comput..

[23]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[24]  Huiqun Zhang,et al.  New exact travelling wave solutions to the complex coupled KdV equations and modified KdV equation , 2008 .

[25]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[26]  Zhenya Yan.  New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations , 2001 .

[27]  E. Fan,et al.  Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation , 2001 .

[28]  Esipov.  Coupled Burgers equations: A model of polydispersive sedimentation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Jinqiao Duan,et al.  Limit set of trajectories of the coupled viscous Burgers' equations , 1996, Applied Mathematics Letters.

[30]  A. A. Soliman,et al.  Numerical solutions of nonlinear evolution equations using variational iteration method , 2007 .

[31]  S. A. El-Wakil,et al.  Modified extended tanh-function method for solving nonlinear partial differential equations , 2002 .

[32]  A. A. Soliman,et al.  The modified extended tanh-function method for solving Burgers-type equations , 2006 .

[33]  Huiqun Zhang,et al.  A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations , 2009 .

[34]  Clive A. J. Fletcher,et al.  Generating exact solutions of the two‐dimensional Burgers' equations , 1983 .

[35]  A. A. Soliman,et al.  Soliton solution for nonlinear partial differential equations by cosine-function method , 2007 .

[36]  A. A. Soliman,et al.  New applications of variational iteration method , 2005 .

[37]  M. A. Abdoua,et al.  Variational iteration method for solving Burger ’ s and coupled Burger ’ s equations , 2005 .

[38]  Zhenya Yan,et al.  New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water , 2001 .