New Miura type transformations between integrable dispersive wave equations

Abstract In this paper, an algebraic method is devised to construct new Miura type transformations between integrable dispersive wave equations. The characteristic feature of our method lies in that the travelling wave solutions of an aimed equation can be determined by the solutions of a simpler equation directly. Our work is an attempt in searching for travelling solutions of complicate nonlinear equations.

[1]  Lixin Tian,et al.  The bifurcation and peakon for K(2, 2) equation with osmosis dispersion , 2009 .

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

[3]  Benchawan Wiwatanapataphee,et al.  On exact travelling wave solutions for two types of nonlinear K(n,n) equations and a generalized KP equation , 2008 .

[4]  Lixin Tian,et al.  Shock-peakon and shock-compacton solutions for K(p,q) equation by variational iteration method , 2007 .

[5]  E. Fan,et al.  Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics , 2003 .

[6]  K. Lonngren,et al.  On the propagation of nonlinear solitary waves in a distributed Schottky barrier diode transmission line , 2001 .

[7]  Komatsu,et al.  Kink soliton characterizing traffic congestion. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Abdul-Majid Wazwaz,et al.  Exact special solutions with solitary patterns for the nonlinear dispersive K(m,n) equations , 2002 .

[9]  Robert M. Miura,et al.  Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation , 1968 .

[10]  D. Burton,et al.  On the Nonlinear Schrodinger Equation for Langmuir Waves , 1973 .

[11]  Abdul-Majid Wazwaz,et al.  New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations , 2002 .

[12]  Yuri S. Kivshar,et al.  Dynamics of Solitons in Nearly Integrable Systems , 1989 .

[13]  Yoshikazu Giga,et al.  Nonlinear Partial Differential Equations , 2004 .

[14]  Abdul-Majid Wazwaz,et al.  A reliable treatment of the physical structure for the nonlinear equation K(m, n) , 2005, Appl. Math. Comput..

[15]  Zhenya Yan,et al.  Painlevé analysis, auto-Bäcklund transformations and exact solutions for a simplified model for reacting mixtures , 2003 .

[16]  Lixin Tian,et al.  Soliton solution of the osmosis K(2,2)K(2,2) equation , 2008, 0907.5522.

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

[18]  M. Jamshidi,et al.  Exact and analytical solution for nonlinear dispersive K(m,p) equations using homotopy perturbation method , 2007 .

[19]  Darryl D. Holm,et al.  An integrable shallow water equation with linear and nonlinear dispersion. , 2001, Physical review letters.