Lax integrability and nonlinear dispersive wave phenomenon for the (3 + 1) dimensional Kudryashov–Sinelshchikov equation

A (3 + 1) dimensional Kudryashov–Sinelshchikov equation is investigated in this paper, which describes bubbles in the liquid fluctuations. By virtue of the binary Bell polynomials, the bilinear representation, bilinear Bäcklund transformation with associated Lax pair are obtained, respectively. Moreover, utilizing Hirota’s bilinear representation, four new lump solutions are constructed and the interaction phenomenon between lump and periodic solution is thoroughly examined. The work also illustrates the intriguing dynamical behavior with the aid of Maple software, which plots the three-dimensional surface, two-dimensional density, and contour profiles of the solutions constructed in this work in various planes.