A generalized nonlinear Schr\"odinger equation as model for turbulence, collapse, and inverse cascade

TL;DR

This paper introduces a generalized nonlinear Schrödinger equation to model complex phenomena like turbulence, collapse, and inverse cascade in two-dimensional wave systems, revealing diverse evolution pathways of localized perturbations.

Contribution

It develops a new generalized equation with complex coefficients to explore various nonlinear wave phenomena and their evolution pathways.

Findings

Modulation leads to side-band formation and wave condensation.

The system exhibits collapse, turbulence, and inverse cascade behaviors.

Not all phenomena occur simultaneously or in a fixed sequence.

Abstract

A two-dimensional generalized cubic nonlinear Schr\"odinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is found that modulation of the latter can lead to side-band formation, wave condensation, collapse, turbulence, and inverse cascade, although not all together nor in that order.