Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Chowdury, Amdad
Institution: Nanyang Technological University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4297793523