Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

TL;DR

This paper explores complex wave solutions in a (2+1)-dimensional graded-index waveguide, revealing new types of rogue waves, soliton pairs, and breathers through similarity transformations of the variable coefficient coupled nonlinear Schrödinger equation.

Contribution

It introduces semirational, multi-parametric solutions including rogue waves and soliton pairs in a (2+1)-D waveguide model using similarity transformations.

Findings

Existence of semirational rogue wave solutions.

Identification of symbiotic soliton pairs with specific coefficient conditions.

Discovery of self-similar breathers and rogue waves when wave components are proportional.

Abstract

We have investigated the ($2+1$)-dimensional variable coefficient coupled nonlinear Schr\"{o}dinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation (SPM) and cross-phase modulation (XPM) coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers and rogue waves as different solutions.