Controllable Kuznetsov Ma-like breather generation via dispersion modulation in the nonlinear Schr\"{o}dinger equation with variable coefficients

TL;DR

This paper explores how dispersion modulation in the variable coefficient nonlinear Schrödinger equation enables controlled generation of Kuznetsov-Ma-like breathers, revealing new features in higher-order rational solutions for applications in optics and Bose-Einstein condensates.

Contribution

It demonstrates the control of rational soliton solutions, including breathers, through dispersion modulation, introducing new features in third-order solutions.

Findings

Controlled generation of first and second-order KM-like breathers via dispersion modulation.

Amplitude and spatial frequency of dispersion control breather properties.

New features observed in third-order rational soliton solutions.

Abstract

The nonlinear Schr\"{o}dinger equation with variable coefficients has applications in numerous areas of physics,specifically in the context of nonlinear optics and Bose-Einstein condensate. Apart from the usual bright and dark-soliton solutions, the so-called rational soliton solutions are perceived to have tremendous impact in futuristic applications and understanding many natural phenomena. In this work, we have studied various orders of rational solution of the variable coefficient nonlinear Schr\"{o}dinger equation. It is possible to extract the first and the second-order controlled KM-like breather by periodic modulation of the dispersion along the propagation direction. The amplitude of the dispersion modulation controls the background as well as the breather peak power in the case of the first-order rational soliton solution, whereas the spatial frequency controls the breathing frequency of the KM-like breather. Our study reveals that it is possible to obtain various new features in the third order rational soliton by modulating the dispersion parameter.