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arXiv · 2412.03502

A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schr\"odinger Equation for Laser Pulse Propagation in Waveguides

Ankit Chakraborty·Judit Munoz-Matute·Leszek Demkowicz·Jake Grosek
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Abstract

In this article, we propose a modified nonlinear Schr\"odinger equation for modeling pulse propagation in optical waveguides. The proposed model bifurcates into a system of elliptic and hyperbolic equations depending on waveguide parameters. The proposed model leads to a stable first-order system of equations, distinguishing itself from the canonical nonlinear Schr\"odinger equation. We have employed the space-time discontinuous Petrov-Galerkin finite element method to discretize the first-order system of equations. We present a stability analysis for both the elliptic and hyperbolic systems of equations and demonstrate the stability of the proposed model through several numerical examples on space-time meshes.

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Ankit Chakraborty, Judit Munoz-Matute, Leszek Demkowicz, Jake Grosek. 2024-12-04. A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schr\"odinger Equation for Laser Pulse Propagation in Waveguides. https://arxiv.org/abs/2412.03502

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