On the continuous limits and integrability of a new coupled semidiscrete mKdV system

Abstract

In this paper, we aim to get more insight on the relation between semidiscrete coupled mKdV system (where “semidiscrete” means that the system is discrete in the space variable and continuous in time) and the coupled mKdV equations; to this purpose, we propose a new coupled semidiscrete mKdV system. The Lax pairs, the Darboux transformation, soliton solutions and conservation laws for the coupled semidiscrete mKdV system are given. The coupled mKdV theory including the Lax pairs, the Darboux transformation, soliton solutions, and conservation laws is recovered through the continuous limits of corresponding theory for the new semidiscrete mKdV system.