Higher-order modulation instability in a fourth-order Nonlinear Schrödinger Equation

2022/09/09 by Chowdury, Amdad
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2209.04200

Abstract

We present a complete dynamical description of the higher-order modulation instability for a fourth-order nonlinear Schrödinger equation. For two-breather solutions of this equation, we have identified the locus in a geometrical space where the growth rates for the breathers are equal in parameter space. We show that a circle bounds the entire parameter space for the nonlinear Schrödinger equation. In contrast, it is bound by an intersecting circle and an ellipse for the fourth-order equation. We show that, for all the higher-order equations in the nonlinear Schrödinger equation hierarchy, the parameter space follows a similar geometric interpretation as for the fourth-order equation.

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