Dynamic behavior of the (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff equation

Abstract

In this article, the (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff equation, which describes the interactions of long wave propagations and has diverse applications in physics, mathematics and engineering, is investigated. Lump and multi-lump wave solutions, one-, and two-soliton solutions, exploding and periodic wave solutions, localized and breather wave solutions, and interaction of lump waves with solitary waves are constructed through the symbolic computational method. In addition, multi-soliton solutions in complex form via using Hirota's simple method and long-wave method are obtained. The dynamic behaviors of all obtained solutions are analyzed and illustrated in figures by choosing appropriate values of the parameters all of the obtained solutions are verified by a direct substitution in the original equation.