Integrability and multiple kinks, lumps, and breathers solutions to an extended (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff fluid model

Abstract This study focuses on analyzing a newly constructed extended (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) fluid model. The Painlevé test is employed to verify the integrability of this newly extended model. We demonstrate that the inclusion of additional terms does not kill the integrability of the standard model. Hirota’s bilinear approach is employed to formally determine multiple soliton \kink solutions. In addition, we rigorously investigate the particular conditions of the parameters to provide lump solutions. In contrast to lump solutions, we obtain breather wave solutions without any requirement for constraints on the used parameters. Various techniques, including the family of tanh and tan procedures, are used to derive different traveling wave solutions with differing physical structures. The obtained solutions are examined and numerically discussed for several arbitrary functions.