Article citationsMore>>

Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press.
https://www.cambridge.org/core/books/direct-method-in-soliton-theory/

has been cited by the following article:

• 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.