A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schrödinger Equation for Laser Pulse Propagation in Waveguides
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915048210825216 |
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| author | Chakraborty, Ankit Munoz-Matute, Judit Demkowicz, Leszek Grosek, Jake |
| author_facet | Chakraborty, Ankit Munoz-Matute, Judit Demkowicz, Leszek Grosek, Jake |
| contents | In this article, we propose a modified nonlinear Schrödinger 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 Schrödinger 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_03502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schrödinger Equation for Laser Pulse Propagation in Waveguides Chakraborty, Ankit Munoz-Matute, Judit Demkowicz, Leszek Grosek, Jake Numerical Analysis In this article, we propose a modified nonlinear Schrödinger 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 Schrödinger 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. |
| title | A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schrödinger Equation for Laser Pulse Propagation in Waveguides |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.03502 |