Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients

TL;DR

This paper derives analytical nonautonomous rogue wave solutions for the inhomogeneous nonlinear Schrödinger equation with variable coefficients, revealing mechanisms for rogue wave formation in various physical contexts.

Contribution

It introduces a method to obtain rational-like solutions for the inhomogeneous nonlinear Schrödinger equation, expanding understanding of rogue wave phenomena in complex systems.

Findings

Derived explicit nonautonomous rogue wave solutions.

Illustrated interactions and propagation traces of rogue waves.

Suggested potential experimental and application relevance.

Abstract

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained solutions can be used to describe the possible formation mechanisms for optical, oceanic, and matter rogue wave phenomenon in optical fibres, the deep ocean, and Bose-Einstein condensates, respectively. Moreover, the snake propagation traces and the fascinating interactions of two nonautonomous rogons are generated for the chosen different parameters. The obtained nonautonomous rogons may excite the possibility of relative experiments and potential applications for the rogue wave phenomenon in the field of nonlinear science.