Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative
Anwar Ali Aldhafeeri, Muneerah Al Nuwairan
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.
Topics & Concepts
Integrable systemBifurcationNonlinear Schrödinger equationFractional calculusNonlinear systemRogue waveMathematical physicsMathematical analysisPlanarBifurcation theoryMathematicsDegeneracy (biology)Derivative (finance)Order (exchange)PhysicsSchrödinger equationQuantum mechanicsComputer scienceBioinformaticsBiologyEconomicsComputer graphics (images)FinanceFinancial economicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems