New interaction solutions of multiply periodic, quasi-periodic and non-periodic waves for the (n + 1)-dimensional double sine-Gordon equations

Abstract New exact solutions with built-in arbitrary functions for the (n + 1)-dimensional double sine-Gordon equation are studied by means of auxiliary solutions of the cubic nonlinear Klein–Gordon (CNKG) fields. By a proper selection of the arbitrary functions and the appropriate solutions of the CNKG systems, new solutions including periodic-solitoffs, periodic-twisted kinks, quasi-periodic and non-periodic waves are obtained.

[1]  Xiao-yan Tang,et al.  Variable separation solutions obtained from Darboux Transformations for the asymmetric Nizhnik–Novikov–Veselov system , 2004 .

[2]  S. Y. Lou,et al.  Revisitation of the localized excitations of the (2+1)-dimensional KdV equation , 2001 .

[3]  C. A. Condat,et al.  Double sine-Gordon chain , 1983 .

[4]  V. Dubrovsky,et al.  A Dimensional Integrable Generalization of the Sine-Gordon Equation I. -∂-Dressing and the Initial Value Problem , 1993 .

[5]  S. Lou.  On the coherent structures of the Nizhnik–Novikov–Veselov equation , 2000 .

[6]  S. Lou,et al.  Extended multilinear variable separation approach and multivalued localized excitations for some (2+1)-dimensional integrable systems , 2003 .

[7]  V. Dubrovsky,et al.  New solutions of two-dimensional integrable sine–Gordon equation generated by nontrivial singular boundaries , 2001 .

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

[9]  Boris Konopelchenko,et al.  The 2+1 dimensional integrable generalization of the sine-Gordon equation. II. Localized solutions , 1993 .

[10]  S. Lou,et al.  DROMION-LIKE STRUCTURES IN A (3 + 1)-DIMENSIONAL KDV-TYPE EQUATION , 1996 .

[11]  Pradeep Kumar,et al.  Magnetic solitons in superfluid 3 He , 1976 .

[12]  R. Dodd,et al.  Multisoliton solutions of nonlinear dispersive wave equations not soluble by the inverse method , 1975 .

[13]  Wen-Xiu Ma,et al.  Diversity of exact solutions to a restricted Boiti-Leon-Pempinelli dispersive long-wave system , 2003 .

[14]  K. Babu Joseph,et al.  Composite mapping method for generation of kinks and solitons in the Klein-Gordon family , 1984 .

[15]  G. Lamb.  Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium , 1971 .

[16]  M. Remoissenet.  Non-linear excitations in a compressible chain of dipoles , 1981 .

[17]  A R Bishop,et al.  Solitons in Condensed Matter Physics , 1979 .

[18]  S. Lou.  (2 + 1)-dimensional compacton solutions with and without completely elastic interaction properties , 2002 .

[19]  S. Lou,et al.  Deforming some special solutions of the sine-Gordon equation to that of the double sine-Gordon equation , 1989 .

[20]  Ying Zhang,et al.  Localized excitations in (2+1)-dimensional systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  S. Lou,et al.  Localized excitations of the (2 + 1)-dimensional sine-Gordon system , 2003 .