A coupled Ramani equation: multiple soliton solutions

In this work, a sixth-order coupled Ramani equation is investigated. The simplified form of the Hirota’s method is used for analytic treatment of this equation. The constraint condition between coefficients of the spatial and the temporal variables is treated. Multiple soliton solutions and multiple singular soliton solutions are formally derived for this model.

[1]  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..

[2]  Wen-Xiu Ma,et al.  Pfaffianized systems for a generalized Kadomtsev–Petviashvili equation , 2013 .

[3]  Mehdi Dehghan,et al.  A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions , 2008, Math. Comput. Simul..

[4]  Abdul-Majid Wazwaz.  Multiple soliton solutions for a new coupled Ramani equation , 2011 .

[5]  B. Kupershmidt,et al.  KdV6: An integrable system , 2007, 0709.3848.

[6]  Kuhn.  Solitons, polarons, and excitons in polyacetylene: Step-potential model for electron-phonon coupling in pi -electron systems. , 1989, Physical review. B, Condensed matter.

[7]  Jibin Li,et al.  Existence of Exact Families of Traveling wave solutions for the Sixth-Order Ramani equation and a Coupled Ramani equation , 2012, Int. J. Bifurc. Chaos.

[8]  J. Brédas,et al.  Polarons, bipolarons, and solitons in conducting polymers , 1985 .

[9]  Ryogo Hirota,et al.  Resonance of Solitons in One Dimension , 1983 .

[10]  M. Khalique.  Exact solutions and conservation laws of a coupled integrable dispersionless system , 2012 .

[11]  Mehdi Nadjafikhah,et al.  Lie symmetries and conservation laws of the Hirota–Ramani equation , 2011, 1111.5178.

[12]  Wenxiu Ma,et al.  Bilinear Equations and Resonant Solutions Characterized by Bell Polynomials , 2013 .

[13]  L. Tolbert.  Solitons in a Box: The Organic Chemistry of Electrically Conducting Polyenes , 1992 .

[14]  Willy Hereman,et al.  Symbolic methods to construct exact solutions of nonlinear partial differential equations , 1997 .

[15]  Wen-Xiu Ma,et al.  Computers and Mathematics with Applications Linear Superposition Principle Applying to Hirota Bilinear Equations , 2022 .

[16]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[17]  Sergei Sakovich,et al.  A new integrable generalization of the Korteweg–de Vries equation , 2007, 0708.3247.

[18]  Wen-Xiu Ma,et al.  Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation , 2011, Appl. Math. Comput..

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

[20]  M. Dehghan.  The one-dimensional heat equation subject to a boundary integral specification , 2007 .

[21]  A. Ramani,et al.  INVERSE SCATTERING, ORDINARY DIFFERENTIAL EQUATIONS OF PAINLEVÉ‐TYPE, AND HIROTA'S BILINEAR FORMALISM * , 1981 .

[22]  Abdul-Majid Wazwaz,et al.  Multiple soliton solutions for the sixth-order Ramani equation and a coupled Ramani equation , 2010, Appl. Math. Comput..

[23]  Robert A. Van Gorder,et al.  Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6 , 2010, Appl. Math. Comput..

[24]  L. Tolbert.  Solitons in a Box: The Organic Chemistry of Electrically Conducting Polyenes , 1992 .

[25]  Wenxiu Ma,et al.  A multiple exp-function method for nonlinear differential equations and its application , 2010, 1010.3324.