Mathematics

CLC number: O175.2

Double-Pole Solution and Soliton-Antisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method

基于Hirota方法的MNLS/DNLS方程的双极点解和孤子-反孤子对

¹ School of Physics, Nanjing University, Nanjing 210023, Jiangsu, China
² School of Physics and Technology, Wuhan University, Wuhan 430072, Hubei, China

^† Corresponding author. E-mail: zgq@whu.edu.cn

Received: 27 November 2023

Abstract

Hirota method is applied to solve the modified nonlinear Schrödinger equation/the derivative nonlinear Schrödinger equation (MNLSE/DNLSE) under nonvanishing boundary conditions (NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.

摘要

本文运用Hirota 方法求解非零边界条件下的修正的非线性薛定谔方程与导数非线性薛定谔方程 (MNLSE/DNLSE)的显式的单极点与双极点孤子解，阐述了Hirota方法求解方程的一般过程以及通过参数极限求得孤子-反孤子对的方法，并分析了解的时空演化图和微扰项、背景振动幅度对解的影响。