The generation mechanism of multiple-pole solutions for the fifth-order mKdV equation

A skillful partial limit approach is proposed in this paper, which is used to generate some new solutions called multiple-pole solutions directly from the well-known N-soliton solution for the fifth-order modified Korteweg-de Vries equation. Based on the traditional limit method developed by us, the dark double-pole solution neglected by some scholars is found. Furthermore, we creatively give a general method for constructing triple-pole solutions, multiple-pole solutions and degeneration of breather solutions. Moreover, the dynamical properties of these multiple-pole solutions are discussed in detail.

Automated summary

In this paper, a skillful partial limit approach is proposed to generate new solutions, called multiple-pole solutions, directly from the well-known N-soliton solution for the fifth-order modified Korteweg-de Vries equation. By applying the traditional limit method, the neglected dark double-pole solution is found. Additionally, a general method for constructing triple-pole solutions, multiple-pole solutions, and degeneration of breather solutions is creatively provided. Furthermore, the dynamic properties of these multiple-pole solutions are thoroughly discussed.