Study of the N-Soliton Solutions for the (2+1)-Dimensional Generalized Caudrey–Dodd–Gibbon–Kotera–Sawada Equation

This paper investigates the N-soliton solutions of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation. By virtue of the Hirota bilinear method, the bilinear form of the equation is derived, and the analytical expression for its N-soliton solutions is constructed. When 𝑁≥2 , with reasonable parameter constraints and appropriate parameter selections, the multi-soliton solutions can degenerate into other types of solitons and exhibit the nonlinear interaction characteristics between different solitons. For instance, two-line solitons can transform into a periodic soliton, and a two-kink soliton can simplify to a kink breather soliton. Three line solitons can present the interaction between a line soliton and a periodic soliton. In contrast, a three-kink soliton can exhibit the interaction between a single-kink soliton and a kink breather soliton. Meanwhile, the four-soliton solution can effectively describe the collision and evolution processes between two line solitons and one periodic soliton, as well as the interaction between two periodic solitons. In addition, applying the long-wave limit method yields lump soliton solutions, and the interaction mechanism between lump solitons and line solitons is examined. Numerical simulations are conducted for the derived soliton structures, and their spatial evolution diagrams are presented. Furthermore, the dynamic characteristics and propagation rules of these solitons are systematically investigated. This finding enriches the solutions to this equation, broaden research on soliton categories and interaction mechanisms, and offer theoretical references for analyzing relevant nonlinear physical models.