Painlevé analysis, integrability property and multiwave interaction solutions for a new (4+1)-dimensional KdV–Calogero–Bogoyavlenkskii–Schiff equation

In this letter a novel (4+1)-dimensional KdV–Calogero–Bogoyavlenkskii–Schiff (KdV-CBS) equation is investigated. The Painlevé analysis shows that this higher dimensional nonlinear equation passes the integrability test. Its integrable properties, including bilinear Bäcklund transformation, Lax pair as well as N-soliton solution, are systematically derived using the binary Bell polynomial method. Furthermore, incorporating the inheritance solving technique into direct algebraic method, we construct the multiwave solutions of 1-lump and (N−2)-soliton (N>2). Multiple choices of parameters in the obtained solutions lead to rich interactions among lump waves, kink waves and breather waves. Several interesting interactions of the multiwave solutions are shown by graphs.