Negative‐order modified KdV equations: multiple soliton and multiple singular soliton solutions

Abstract

In this work, we develop the negative‐order modified Korteweg–de Vries (nMKdV) equation. By means of the recursion operator of the modified KdV equation, we derive negative order forms, one for the focusing branch and the other for the defocusing form. Using the Weiss–Tabor–Carnevale method and Kruskal's simplification, we prove the Painlevé integrability of the nMKdV equations. We derive multiple soliton solutions for the first form and multiple singular soliton solutions for the second form. Copyright © 2015 John Wiley & Sons, Ltd.