Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative

In this paper, we investigate the time M-fractional modified nonlinear Schrödinger equation that describes the propagation of rogue waves in deep water. Periodic, solitary, and kink (or anti-kink) wave solutions are discussed using the bifurcation theory for planar integrable systems. Some new wave...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 5; p. 1219
Main Authors Aldhafeeri, Anwar, Al Nuwairan, Muneerah
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2023
Subjects
bifurcation analysis
Bifurcation theory
Deep water
Differential equations
fractional derivatives
Graphical representations
Gravitational waves
Orbits
phase space
Schrodinger equation
Schrödinger equation
soliton solution
Traveling waves
Water waves
Wave propagation
Saudi Arabia
Online AccessGet full text

Cover

More Information
Summary:In this paper, we investigate the time M-fractional modified nonlinear Schrödinger equation that describes the propagation of rogue waves in deep water. Periodic, solitary, and kink (or anti-kink) wave solutions are discussed using the bifurcation theory for planar integrable systems. Some new wave solutions are constructed using the first integral for the traveling wave system. The degeneracy of the obtained solutions is investigated by using the transition between orbits. We visually explore some of the solutions using graphical representations for different values of the fractional order.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11051219