Darboux transformation and solution of the modified Korteweg–de Vries equation

Abstract

Darboux transformation and a comprehensive approach to construct exact solutions of the nonlinear differen-tial equation are counted. It is applied to construct the explicit solutions of the (2+1)-dimensional modified Korteweg–de Vries (KdV) equation. In this work we derive one flod Darboux transformation of the modified KdV equation. Using the obtained Darboux transformation, the one-soliton solution is built from the «seed» solution. Further, we will construct other explicit solutions for this equation.