Abstract

In this paper, the generalized fifth-order Kaup–Kupershmidt (KK) equation from the shallow water wave, have been investigated. With the help of bilinear method and auxiliary function, the multi-soliton solutions of the generalized fifth-order KK equation have been obtained, and those solutions have not been given before. From the analytical view, the interactions of the solitons have been presented. Through the discussion, we have found that the velocity of the soliton is related to the sign of the physical parameters \(b\) and \({{c}_{j}}\). Also, the (bright or dark-like) types of the soliton interaction are related to the physical parameters \(a\). Hence, the velocities and bright-dark types of the soliton interactions could be controlled by adjusting the physical parameters.

中文翻译：

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浅水波广义五阶Kaup-Kupershmidt方程的解析研究

摘要

本文研究了浅水波的广义五阶Kaup–Kupershmidt（KK）方程。借助于双线性方法和辅助函数，获得了广义五阶KK方程的多孤子解，而以前没有给出。从分析的角度，提出了孤子的相互作用。通过讨论，我们发现了孤子的速度与物理参数\（b \）和\（{{{c} _ {j}} \\）的符号有关。同样，孤子相互作用的（亮或暗）类型与物理参数\（a \）相关。因此，可以通过调节物理参数来控制孤子相互作用的速度和明暗类型。