A (3+1)-dimensional integrable Calogero-Bogoyavlenskii-Schiff equation and its inverse operator: lump solutions and multiple soliton solutions

Abstract

"In this work, we built a (3+1)-dimensional integrable equation. We started by reformulating the main equation of our model by combining the recursion operator of the Calogero-Bogoyavlenskii-Schiff equation with its inverse recursion op- erator. We confirm the complete integrability of our new developed equation by demon- strating that it satisfies the Painlev´e property. We get a variety of lump solutions that are obtained under specific constraints. Furthermore, we used the simplified Hirota’s direct approach to find multiple soliton solutions to the new evolution equation. In ad- dition, other techniques are used to solve the new evolution equation, in order to get some physically relevant solutions."