Bilinear form and soltion solutions for (3+1)-dimensional negative-order KdV-CBS equation

Abstract This article investigates a significant mathematical model for multiwave interactions. For the first time, the bilinear form of the (3+1)-dimensional negative-order Korteweg–de Vries (KdV)-Calogero–Bogoyavlenskii–Schiff (CBS) equation is derived using binary Bell polynomials, and 1, 2, and 3-soliton solutions are obtained through this bilinear form. These solutions are further visualized via 3D and 2D plots representations. This study fills a research gap in this direction and demonstrates that the results can significantly enhance the efficiency of obtaining diverse solutions for the (3+1)-dimensional negative-order KdV-CBS equation. It is anticipated that these solutions will not only deepen our understanding of the physical phenomena associated with the equation but also reveal more complex physical behaviors, thereby advancing analytical studies on solutions to other nonlinear partial differential equations.