Compact structures for variants of the generalized KdV and the generalized KP equations

In this paper we discuss mathematical variants in higher dimensions of the generalized KdV and the generalized KP equations. It is shown that the focusing branches of these variants exhibit compactons: solitons with finite wavelength, whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps. The compact and the noncompact dispersive structures are examined in a general way.

[1]  Abdul-Majid Wazwaz,et al.  A computational approach to soliton solutions of the Kadomtsev-Petviashvili equation , 2001, Appl. Math. Comput..

[2]  Abdul-Majid Wazwaz,et al.  General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces , 2002, Appl. Math. Comput..

[3]  Abdul-Majid Wazwaz,et al.  Compact and noncompact structures in a class of nonlinearly dispersive equations , 2003, Math. Comput. Simul..

[4]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[5]  Abdul-Majid Wazwaz,et al.  Partial differential equations : methods and applications , 2002 .

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

[7]  Abdul-Majid Wazwaz,et al.  Compactons and solitary patterns structures for variants of the KdV and the KP equations , 2003, Appl. Math. Comput..

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

[9]  Abdul-Majid Wazwaz,et al.  General compactons solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher-dimensional spaces , 2002, Appl. Math. Comput..

[10]  A. Wazwaz.  A First Course in Integral Equations , 1997 .

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

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

[13]  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.

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

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

[16]  M. Wadati,et al.  The Modified Korteweg-de Vries Equation , 1973 .

[17]  Mathieu S. Capcarrère,et al.  Necessary conditions for density classification by cellular automata. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  J M Hyman,et al.  Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[20]  M. S. Ismail,et al.  A numerical study of compactons , 1998 .

[21]  M. Wadati.  Introduction to solitons , 2001 .

[22]  G. Adomian.  A review of the decomposition method in applied mathematics , 1988 .

[23]  A. Wazwaz.  Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method , 2001 .

[24]  A. Wazwaz.  A study of nonlinear dispersive equations with solitary-wave solutions having compact support , 2001 .

[25]  M. Wadati,et al.  The Exact Solution of the Modified Korteweg-de Vries Equation , 1972 .