(2+1)-Dimensional mKdV (N) equations by the mKdV recursion operator: Multiple soliton and multiple singular soliton solutions

In this work we present a new variety of (2+1)-dimensional mKdV (N) equations with distinct even orders. We use the recursion operator of the mKdV equation to develop achieve this goal. We show that these equations give multiple soliton solutions and multiple singular soliton solutions the same as the multiple soliton and multiple singular soliton solutions of the mKdV hierarchy except for the dispersion relations. We also develop a generalization for the dispersion relations and the order of these equations.

► We establish a variety of (2+1)-dimensional mKdV (N) equations. ► We use the recursion operator of the mKdV equation. ► We derive multiple soliton solutions with distinct dispersion relations.