Analysis of the solitary wave solutions of the negative order modified Korteweg –de Vries equation with a self-consistent source

Abstract

In this work, the initial value problem for the negative order modified Korteweg–de Vries equation (nmKdV) with a self-consistent source was analyzed. The inverse scattering transform method for obtaining evolution equations of scattering data of the Dirac operator, which potential is the solution of the considered problem was implemented. For the first time, the real matrix triplet $(A,B,C)$ method was applied to construct a multisoliton solution of nmKdV equation with a self-consistent source. Furthermore, the wave phenomena of solitons were demonstrated by varying the normalization conditions.