A two-mode modified KdV equation with multiple soliton solutions

Abstract In this work we establish a two-mode modified Korteweg–de Vries equation (TmKdV). We show that multiple soliton solutions exist for specific values of the nonlinearity and dispersion parameters of this equation. We also derive more exact solutions for other values of these parameters. We will use the simplified Hirota’s method, the tanh/coth method to conduct this analysis.

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

[2]  Abdul-Majid Wazwaz,et al.  Multiple kink solutions for two coupled integrable (2+1)-dimensional systems , 2016, Appl. Math. Lett..

[3]  Jinn-Liang Liu,et al.  A Hamiltonian model and soliton phenomenon for a two- mode KdV equation , 2011 .

[4]  A. Wazwaz.  New (3+1)‐dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions , 2016 .

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

[6]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for extended (3+1)-dimensional Jimbo-Miwa equations , 2017, Appl. Math. Lett..

[7]  T. Hyde,et al.  Using dust as probes to determine sheath extent and structure , 2016, Journal of Plasma Physics.

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

[9]  C. Lee,et al.  On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system , 2013 .

[10]  S. Korsunsky.  Soliton solutions for a second-order KdV equation , 1994 .

[11]  Suheil A. Khuri,et al.  Soliton and periodic solutions for higher order wave equations of KdV type (I) , 2005 .

[12]  A. eman.  Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas , 2016 .

[13]  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..