New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations

Abstract The special exact solutions of nonlinearly dispersive Boussinesq equations (called B ( m , n ) equations), u tt − u xx − a ( u n ) xx + b ( u m ) xxxx =0, is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with m =1. Moreover, another new compacton solution of the special case, B (2,2) equation, is also found.

[1]  Philip Rosenau,et al.  On solitons, compactons, and Lagrange maps , 1996 .

[2]  Philip Rosenau,et al.  Compact and noncompact dispersive patterns , 2000 .

[3]  P. Olver,et al.  Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[5]  B. Dey,et al.  Compacton solutions for a class of two parameter generalized odd-order Korteweg-de Vries equations , 1998 .

[6]  D. Levy,et al.  Compactons in a class of nonlinearly quintic equations , 1999 .

[7]  P. Rosenau,et al.  Nonlinear dispersion and compact structures. , 1994, Physical review letters.

[8]  Abdul-Majid Wazwaz,et al.  Compactons dispersive structures for variants of the K(n,n) and the KP equations , 2002 .

[9]  P. T. Dinda,et al.  Breather compactons in nonlinear Klein-Gordon systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[11]  Philip Rosenau,et al.  On a class of nonlinear dispersive-dissipative interactions , 1997 .

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

[13]  Ryogo Hirota,et al.  Exact N‐soliton solutions of the wave equation of long waves in shallow‐water and in nonlinear lattices , 1973 .

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

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