Multiple-soliton solutions for extended (3+1)-dimensional Jimbo-Miwa equations

Abstract In this work we investigate two extended ( 3 + 1 ) -dimensional Jimbo–Miwa equations. We use the simplified Hirota’s method to derive multiple soliton solutions of distinct physical structures for each extended equation. We show that the dispersion relations and the phase shifts of the extended equations are distinct compared to the dispersion and shifts of the Jimbo–Miwa equation.

[1]  C. M. Khalique,et al.  Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities , 2013 .

[2]  M. Najafi,et al.  Some Complexiton Type Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation , 2011 .

[3]  Wenxiu Ma,et al.  A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation , 2009, 0903.5337.

[4]  Chaudry Masood Khalique,et al.  Exact solutions of the (2+1 )-dimensional Zakharov-Kuznetsov modified equal width equation using Lie group analysis , 2011, Math. Comput. Model..

[5]  M. Jimbo,et al.  Solitons and Infinite Dimensional Lie Algebras , 1983 .

[6]  Bintao Cao.  Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations , 2009, 0902.3308.

[7]  Abdul-Majid Wazwaz,et al.  New (3+1)-dimensional nonlinear evolution equations with mKdV equation constituting its main part: Multiple soliton solutions , 2015 .

[8]  A. Wazwaz.  Soliton solutions of the dispersive sine-Gordon and the dispersive sinh-Gordon equations with fourth spatial or spatio-temporal derivatives , 2011 .

[9]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations , 2008, Appl. Math. Comput..

[10]  Bao-Zhu Zhao,et al.  Exact rational solutions to a Boussinesq-like equation in (1+1)-dimensions , 2015, Appl. Math. Lett..

[11]  Dumitru Mihalache,et al.  Few-optical-cycle solitons: Modified Korteweg-de Vries sine-Gordon equation versus other non-slowly-varying-envelope-approximation models , 2009 .

[12]  P. Olver,et al.  Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations , 1992 .

[13]  Abdul-Majid Wazwaz,et al.  A KdV6 hierarchy: Integrable members with distinct dispersion relations , 2015, Appl. Math. Lett..

[14]  Abdul-Majid Wazwaz.  A study on the (2+1)-dimensional and the (2+1)-dimensional higher-order Burgers equations , 2012, Appl. Math. Lett..

[15]  A. Neirameh,et al.  New soliton solutions to the (3+1)-dimensional Jimbo–Miwa equation , 2015 .

[16]  Abdul-Majid Wazwaz.  Multiple soliton solutions for some (3+1 )-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy , 2012, Appl. Math. Lett..

[17]  A. Wazwaz.  Partial Differential Equations and Solitary Waves Theory , 2009 .

[18]  Dumitru Mihalache,et al.  Models of few optical cycle solitons beyond the slowly varying envelope approximation , 2013 .

[19]  Guiqiong Xu,et al.  The soliton solutions, dromions of the Kadomtsev–Petviashvili and Jimbo–Miwa equations in (3 + 1)-dimensions , 2006 .

[20]  C. M. Khalique,et al.  Nonlinear evolution-type equations and their exact solutions using inverse variational methods , 2005 .