D. Aravindha Krishnan

arXiv2026

PINN-Based Framework for Soliton Solutions of Gross Pitaevskii and Nonlinear Schrodinger Equations

This study presents a data-driven framework for solving nonlinear wave equations, specifically the Gross-Pitaevskii equation (GPE) and the single-component nonlinear Schrodinger equation (NLSE), using Physics-Informed Neural Networks (PINNs). The approach integrates physical constraints directly into the neural network's loss function, enabling efficient training without requiring labelled data. We implement a PINN-based framework for solitons that models a variety of localized wave structures across both equations. Predicted solutions are compared with exact analytical results and show strong agreement with low error. The method effectively captures soliton profiles in both the GPE and NLSE. The accuracy and flexibility of the framework suggest its usefulness for studying nonlinear differential equations relevant to Bose--Einstein condensates and nonlinear optics.

nlin.PS↗

arXiv2024

Collisional Dynamics of Solitons and Pattern Formation in an Integrable Cross Coupled Nonlinear Schrodinger equation with constant background

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 Schrodinger 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.

nlin.SI↗