Multiple kink solutions for two coupled integrable (2+1)-dimensional systems

Abstract We obtain multiple kink solutions for two coupled (2+1)-dimensional systems, namely, a coupled Burgers system and a coupled modified KdV–Boiti–Leon–Manna–Pempinelli system, by means of the simplified Hirota’s method. It is demonstrated that the coupled modified KdV–Boiti–Leon–Manna–Pempinelli system gives kink solutions.

[1]  M. S. HASHEMI,et al.  CONSERVATION LAWS AND SYMMETRIES OF mKdV – KP EQUATION , 2015 .

[2]  Anjan Biswas,et al.  Solitary wave solution for the generalized KdV equation with time-dependent damping and dispersion , 2009 .

[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,et al.  Kinks and travelling wave solutions for Burgers-like equations , 2014, Appl. Math. Lett..

[5]  Abdul-Majid Wazwaz,et al.  The generalized KaupߝBoussinesq equation: multiple soliton solutions , 2015 .

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

[7]  Chaudry Masood Khalique,et al.  On the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation , 2013, J. Appl. Math..

[8]  Abdul-Majid Wazwaz,et al.  Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities , 2015, Nonlinear Dynamics.

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

[10]  S. Lou,et al.  Infinitely many Lax pairs and symmetry constraints of the KP equation , 1997 .

[11]  Abdul-Majid Wazwaz.  NEW (3+1)-DIMENSIONAL NONLINEAR EVOLUTION EQUATIONS WITH BURGERS AND SHARMA-TASSO-OLVER EQUATIONS CONSTITUTING THE MAIN PARTS , 2015 .

[12]  Man Jia,et al.  The bilinear negative Kadomtsev–Petviashvili system and its Kac–Moody–Virasoro symmetry group , 2008 .

[13]  Zhengde Dai,et al.  Spatiotemporal deformation of multi-soliton to (2 + 1)-dimensional KdV equation , 2016 .

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

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

[16]  M. Boiti,et al.  On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions , 1986 .

[17]  Chaudry Masood Khalique,et al.  A direct bilinear Bäcklund transformation of a (2+1)-dimensional Korteweg-de Vries-like model , 2015, Appl. Math. Lett..

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

[19]  Wen-Xiu Ma,et al.  Solving the (3 + 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm , 2012, Appl. Math. Comput..

[20]  A. Wazwaz.  The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation , 2008, Appl. Math. Comput..

[21]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[22]  Xiao-yan Tang,et al.  Infinitely many generalized symmetries and Painlevé analysis of a (2 + 1)-dimensional Burgers system , 2014 .

[23]  Abdul-Majid Wazwaz,et al.  Combined equations of the Burgers hierarchy: multiple kink solutions and multiple singular kink solutions , 2010, J. Frankl. Inst..

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

[25]  Saudi Arabia,et al.  ANALYTICAL APPROXIMATE SOLUTIONS OF THE ZAKHAROV-KUZNETSOV EQUATIONS , 2014 .

[26]  Saudi Arabia,et al.  DYNAMICS OF TWO-LAYERED SHALLOW WATER WAVES WITH COUPLED KdV EQUATIONS , 2014 .

[27]  Abdul-Majid Wazwaz,et al.  Kadomtsev-Petviashvili hierarchy: N-soliton solutions and distinct dispersion relations , 2016, Appl. Math. Lett..

[28]  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..

[29]  ANJAN BISWAS,et al.  SOLITARY WAVES AND OTHER SOLUTIONS TO KADOMTSEV-PETVIASHVILI EQUATION WITH SPATIO-TEMPORAL DISPERSION , 2015 .

[30]  Abdul-Majid Wazwaz,et al.  Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers-type equations , 2009 .