TITLE:
Higher-Order Solitions and Their Mixed Interactions for the (2 + 1)-Dimensional KdV Equation
AUTHORS:
Meiling Duan, Keke Chen
KEYWORDS:
KdV-Equation, Bilinear Method, T-Order Breather Solutions, L-Order Lump Solutions, Hybrid Solutions, Collision Trajectories
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.10,
October
30,
2025
ABSTRACT: In this paper, we primarily investigate several exact solutions of the (2 + 1)-dimensional KdV equation and summarize the trajectory equations after collisions between these solutions. Using the bilinear form with specific test functions and the parameter limiting technique, we construct T-order breather solutions, L-order lump solutions, and hybrid solutions. On this basis, we examine the close relationship between the positions of breather solutions and the parameters, the motion trajectories resulting from the interaction of lump solutions, as well as the trajectories of a single lump before and after its collision with higher-order soliton solutions.