A (3+1)-dimensional integrable calogero-bogoyavlenskii-schiff equation and its inverse operator: lump solutions and multiple soliton solutions

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 operator. We confirm the complete integrability of our new developed equation by demonstrating that it satisfies the Painleve 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 addition, other techniques are used to solve the new evolution equation, in order to get some physically relevant solutions.