An improved algebra method and its applications in nonlinear wave equations

Abstract In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation, which is including the algebraic method, is further investigated. By using the solutions of this equation, we give some types of solutions of the coupled KdV equation, nonlinear dispersion mK( m , n , k ) equation, the variant shallow water wave equation, nonlinear dissipative equation and the higher-order nonlinear Schrodinger equation. These solutions includes compacton solutions , solitary pattern solutions , solitary wave solutions , Weierstrass elliptic function solutions , which may be useful to explain some phenomena.

[1]  E. V. Krishnan,et al.  On the Ito-Type Coupled Nonlinear Wave Equation , 1986 .

[2]  Hong-qing Zhang,et al.  New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics , 1999 .

[3]  Agrawal,et al.  Kink solitons and optical shocks in dispersive nonlinear media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  Hyman,et al.  Compactons: Solitons with finite wavelength. , 1993, Physical review letters.

[5]  Manuel G. Velarde,et al.  Exact periodic solutions of the complex Ginzburg-Landau equation , 1999 .

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

[7]  Philip Rosenau,et al.  On nonanalytic solitary waves formed by a nonlinear dispersion , 1997 .

[8]  Zhenya Yan,et al.  The extended Jacobian elliptic function expansion method and its application in the generalized Hirota–Satsuma coupled KdV system , 2003 .

[9]  赵海斌,et al.  Fe 45 Ag 55 颗粒膜的磁光尺寸效应 , 2006 .

[10]  E. V. Krishnan,et al.  AN EXACT SOLUTION OF THE CLASSICAL BOUSSINESQ EQUATION , 1982 .

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

[12]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[13]  Huang Yan,et al.  Nonlinear deformation theory of thin shell , 2000 .

[14]  B. M. Fulk.  MATH , 1992 .

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

[16]  Abdul-Majid Wazwaz,et al.  General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n, n) in higher dimensional spaces , 2002, Math. Comput. Simul..

[17]  Yan Zhen-ya.  New Symmetry Reductions, Dromions-Like and Compacton Solutions for a 2D BS(m,n) Equations Hierarchy with Fully Nonlinear Dispersion , 2002 .

[18]  X. Feng,et al.  Exploratory Approach to Explicit Solution ofNonlinear Evolution Equations , 2000 .

[19]  Yan Zhen-ya.  New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion , 2001 .

[20]  Zhenya Yan,et al.  New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations , 2002 .

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

[22]  Alexey V. Porubov,et al.  Periodical solution to the nonlinear dissipative equation for surface waves in a convecting liquid layer , 1996 .

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

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

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

[26]  C. Guha-Roy,et al.  Solitary wave solutions of a system of coupled nonlinear equations , 1987 .

[27]  S. L. Palacios,et al.  Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[29]  Engui Fan,et al.  Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method , 2002 .

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

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