Solitons, Bäcklund transformation and Lax pair for the (2+1)-dimensional Kaup system

In this paper, we investigate the (2+1)-dimensional Kaup system, a nonlinear integrable model arising in water wave dynamics within narrow channels of constant depth. Utilizing the binary Bell polynomials and Hirota’s bilinear method, we derive the bilinear forms of the system and construct one- and two-soliton solutions. The dynamical properties of these solitons, including their stable propagation and interaction behavior, are graphically analyzed, demonstrating typical soliton features such as shape preservation and elastic collision. Furthermore, we establish the Bäcklund transformation and present the associated Lax pair, confirming the integrability of the system. The results enhance the understanding of multidimensional nonlinear wave phenomena within fluid mechanics and provide analytical tools for exploring related integrable models.