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

Anwar Aldhafeeri and Muneerah Al Nuwairan ()
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Anwar Aldhafeeri: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Muneerah Al Nuwairan: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia

Mathematics, 2023, vol. 11, issue 5, 1-14

Abstract: 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.

Keywords: Schrödinger equation; soliton solution; bifurcation analysis; phase space; fractional derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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