In this work, an algorithm for constructing solutions to the negative order modified Korteweg–de Vries equation is proposed, based on the application of the inverse scattering theory to the Zakharov–Shabat system. Within the framework of the developed algorithm, an explicit one-soliton solution of...

In this paper, we integrate the negative order matrix modified Korteweg-de Vries (KdV) equation with a self-consistent source in the class of rapidly decreasing functions. We derive the temporal dependence of the scattering data of the Dirac operator....