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Modified Korteweg–de Vries equation; combined soliton solution; soliton dynamics.

In this paper, the Riemann–Hilbert problem of the modified Korteweg–de Vries (mKdV) equation is studied, from which a new combined soliton solution is obtained. In addition, to illustrate the dynamics of the new combined soliton solution, an algebra technique is developed to demonstrate the soliton interactions using $Mathematica$ symbolic computations. The proposed method is effective in deriving and investigating new soliton solutions of the mKdV equation. The results also expand the understanding of the soliton structure of the mKdV equation.

JIANPING WU

Published

13 August 2020

Manuscript received

26 November 2019

Manuscript revised

9 February 2020

Accepted

18 February 2020

Final version published online

13 August 2020