VINAYAGAM, P.S (2024) COLLISIONAL DYNAMICS OF SOLITONS AND PATTERN FORMATION IN AN INTEGRABLE CROSS COUPLED NONLINEAR SCHR¨ODINGER EQUATIONWITH CONSTANT BACKGROUND. COLLISIONAL DYNAMICS OF SOLITONS AND PATTERN FORMATION IN AN INTEGRABLE CROSS COUPLED NONLINEAR SCHR¨ODINGER EQUATIONWITH CONSTANT BACKGROUND. ISSN 1221-1451

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Abstract

We investigate the dynamics arising out of the propagation of light pulses with
different polarizations through a condensate (referred to as a constant background field)
with cross coupling described by a coupled nonlinear Schr¨odinger equation(NLSE) type
equation. We then employ Gauge and Darboux transformation approach to bring out the
rich dynamics arising out of the background field and cross coupling. The collisional
dynamics of bright solitons is found to be inelastic. The constant background field
is found to facilitate the periodic localization of light pulses during propagation. We
have also unearthed breathers, bright-bright, bright-dark and dark-bright solitons of the
coupled NLSE. While the amplitude of breathers oscillate with time as predicted, their
maximum(or minimum) amplitude is found to remain a constant and the addition of
cross coupling only contributes to the rapid fluctuations in its amplitude over a period of
time. In addition, the reinforcement of cross coupling in the presence of constant wave
field facilitates the interference of light pulses leading to interesting pattern formation
among bright-bright, bright-dark and dark-bright solitons. The highlight of the results
is that one obtains various localized excitations like breathers, bright and dark solitons
by simply manipulating the amplitude of the constant wave field.

Item Type: Article
Uncontrolled Keywords: Coupled nonlinear Schr¨odinger equation, Gauge transformation, Darboux transformation, Lax pair, Breathers, Solitons
Divisions: PSG College of Arts and Science > Department of Physics
Depositing User: Mr Team Mosys
Date Deposited: 25 Feb 2025 09:43
Last Modified: 25 Feb 2025 09:43
URI: https://ir.psgcas.ac.in/id/eprint/2375

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