Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation

Abstract

In this paper, a (3+1)-dimensional Hirota-Satsuma-Ito-like equation is introduced based on the (2+1)-dimensional Hirota-Satsuma-Ito equation. Bäcklund transformation and corresponding exponential function solutions are deduced by virtue of the Hirota bilinear form. The lump solutions are constructed and the interaction phenomena between a lump wave and multi-kink waves are discussed. The lump wave may turn up in different positions and can be swallowed by multi-kink waves, which means that the collision is non-elastic. Finally, the dynamical behavior of the interaction phenomena is numerically simulated.