New solitonary solutions for the MBBM equations using Exp-function method

Abstract In this Letter we use the Exp-function method for analytic treatment for the modified Benjamin–Bona–Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically change the characteristics of the equations, is examined. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics.

[1]  M. A. Abdou.  The extended F-expansion method and its application for a class of nonlinear evolution equations , 2007 .

[2]  Sheng Zhang,et al.  Symbolic computation and new families of exact non-travelling wave solutions to (3+1)-dimensional Kadomstev-Petviashvili equation , 2006, Appl. Math. Comput..

[3]  Zhang Sheng,et al.  The periodic wave solutions for the (2 + 1)-dimensional dispersive long water equations , 2007 .

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

[5]  Tiecheng Xia,et al.  A further improved extended Fan sub-equation method and its application to the (3+1)-dimensional Kadomstev Petviashvili equation , 2006 .

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

[7]  Ji-Huan He.  Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[8]  A. Wazwaz,et al.  Nonlinear variants of the BBM equation with compact and noncompact physical structures , 2005 .

[9]  Η. A. Abdusalam,et al.  On an Improved Complex Tanh-function Method , 2005 .

[10]  E. Yusufoglu,et al.  Variational Iteration Method for Construction of Some Compact and Noncompact Structures of Klein-Gordon Equations , 2007 .

[11]  Yue Liu,et al.  Cauchy problem for the Ostrovsky equation , 2004 .

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

[13]  Ji-Huan He,et al.  Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method , 2007, Comput. Math. Appl..

[14]  M. A. Abdou,et al.  Modified extended tanh-function method for solving nonlinear partial differential equations , 2007 .

[15]  M. A. Abdou,et al.  NEW PERIODIC SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS USING EXP-FUNCTION METHOD , 2007 .

[16]  E. Yusufoglu,et al.  The variational iteration method for solitary patterns solutions of gBBM equation , 2007 .

[17]  Abdul-Majid Wazwaz,et al.  The tanh method for traveling wave solutions of nonlinear equations , 2004, Appl. Math. Comput..

[18]  Abdelhalim Ebaid,et al.  Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method , 2007 .

[19]  Sheng Zhang,et al.  Application of Exp-function method to a KdV equation with variable coefficients , 2007 .

[20]  Ji-Huan He,et al.  Variational principles for some nonlinear partial differential equations with variable coefficients , 2004 .

[21]  Abdul-Majid Wazwaz,et al.  A sine-cosine method for handlingnonlinear wave equations , 2004, Math. Comput. Model..

[22]  Jean-Claude Saut,et al.  Global well-posedness for the KP-BBM equations , 2004 .

[23]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[24]  M. Tabor,et al.  The Painlevé property for partial differential equations , 1983 .

[25]  M. A. Abdou,et al.  New exact travelling wave solutions using modified extended tanh-function method , 2007 .

[26]  Hu Junqi,et al.  An algebraic method exactly solving two high-dimensional nonlinear evolution equations , 2005 .

[27]  Khaled A. Gepreel,et al.  Group Analysis and Modified Extended Tanh-function to Find the Invariant Solutions and Soliton Solutions for Nonlinear Euler Equations , 2004 .

[28]  J. Bona,et al.  Model equations for long waves in nonlinear dispersive systems , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[29]  Hong-qing Zhang,et al.  Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system , 2006 .

[30]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[31]  Zhang Sheng,et al.  The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equations , 2006 .

[32]  M. El-shahed.  Application of He's Homotopy Perturbation Method to Volterra's Integro-differential Equation , 2005 .

[33]  Emmanuel Yomba,et al.  The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer–Kaup–Kupershmidt equation , 2006 .

[34]  Chao-Qing Dai,et al.  Jacobian elliptic function method for nonlinear differential-difference equations , 2006 .

[35]  Sheng Zhang.  New exact solutions of the KdV–Burgers–Kuramoto equation , 2006 .

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

[37]  Sheng Zhang,et al.  Further improved extended Fan sub-equation method and new exact solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equations , 2006, Appl. Math. Comput..

[38]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[39]  Bounded wave solutions of a generalized BBM equation with positive exponents , 2007 .

[40]  Ji-Huan He.  Homotopy Perturbation Method for Bifurcation of Nonlinear Problems , 2005 .