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arXiv · 2607.22685

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

P. S. Vinayagam·Sai Jeevanth G·D. Aravindha Krishnan·Nithish Kathiravan
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Abstract

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.

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P. S. Vinayagam, Sai Jeevanth G, D. Aravindha Krishnan, Nithish Kathiravan. 2026-07-14. PINN-Based Framework for Soliton Solutions of Gross Pitaevskii and Nonlinear Schrodinger Equations. https://arxiv.org/abs/2607.22685

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