Lax pairs, Darboux transformation, bilinear forms and solitonic interactions for a combined Calogero-Bogoyavlenskii-Schiff-type equation

Abstract Calogero-Bogoyavlenskii-Schiff-type (CBS-type) equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Under investigation in this paper is a combined CBS-type equation. Lax pairs in the differential and matrix forms are derived respectively. Infinite conservation laws, which are different from those in the existing literatures, and n -fold Darboux transformation are constructed through the matrix-form Lax pair, where n is a positive integer. Bilinear forms are constructed. Parallel solitons can be derived from the bilinear forms, which are caused by a constraint in the linearization process. Waveforms for the parallel solitons have the no superposition, nonlinear superposition and linear superposition forms. Bell-to-anti-bell-shaped solitons and oblique solitonic interactions are discovered via the n -fold Darboux transformation. Each bell-shaped asymptotic soliton of the bell-to-anti-bell-shaped soliton evolves into the anti-bell-shaped one.