On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients

TL;DR

This paper develops and analyzes vector rogue wave solutions for two-dimensional coupled nonlinear Schrödinger equations with distributed coefficients, revealing new patterns and characteristics in rogue wave structures.

Contribution

It introduces a method to construct vector rogue wave solutions with distributed coefficients and explores their unique patterns and properties.

Findings

Identified various patterns in rogue wave structures.

Constructed vector dark rogue wave solutions with novel features.

Linked the equations to the Manakov model via similarity transformation.

Abstract

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schr\"{o}dinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.