Painlevé analysis for a new integrable equation combining the modified Calogero–Bogoyavlenskii–Schiff (MCBS) equation with its negative-order form

Abstract

A new integrable equation is constructed by combining the recursion operator of the modified Calogero–Bogoyavlenskii–Schiff equation and its inverse recursion operator. The Painleve is performed to demonstrate the complete integrability of the newly developed equation. Multiple-soliton solutions are depicted as manifestation of the integrability. We further show that this equation enjoys a variety of soliton solutions that include kinks, peakon, cuspon.