Bifurcations and exact solutions of generalized nonlinear Schrödinger equation

To find the exact explicit solutions of the generalized nonlinear Schrödinger equation, we first give the corresponding differential system for the amplitude component, which constitutes a planar dynamical system featuring a singular straight line. By analyzing its corresponding traveling wave syste...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 3; pp. 5158 - 5172
Main Authors Zhang, Qian, Ke, Ai
Format Journal Article
LanguageEnglish
Published AIMS Press 01.03.2025
Subjects
peakon
periodic peakon
periodic wave
solitary wave
traveling wave system
Online AccessGet full text

Cover

More Information
Summary:To find the exact explicit solutions of the generalized nonlinear Schrödinger equation, we first give the corresponding differential system for the amplitude component, which constitutes a planar dynamical system featuring a singular straight line. By analyzing its corresponding traveling wave system, we can derive the dynamical behavior of the amplitude component and give the corresponding phase portraits. Under different parameter conditions, we obtain exact explicit solitary wave solutions, periodic wave solutions, as well as peakons and periodic peakons. By comparing our results with previous studies on the generalized nonlinear Schrödinger equation, we correct the error regarding the first integral and present accurate solutions to the equation.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025237