Analytical and Data-Driven Wave Approximations of an Extended Schrödinger Equation Article Swipe

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Rachel Klauss , Aaron Phillips , José Vega-Guzmán ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.3390/sym14030465

Using both analytical and numerical techniques, we discuss wave solutions within the framework of an extended nonlinear Schrödinger equation with constant coefficients equipped with spatiotemporal dispersion, self-steepening effects, and a Raman scattering term. We present the exact traveling wave solution of the system in terms of Jacobi elliptic functions and mention some symmetry results as they relate to the resulting ordinary differential equation. A constructed bright soliton solution serves as the base to compare a numerical solution of the system using spectral Fourier methods with a precise statistical low-rank approximation using a data-driven approach aided by the Koopman operator theory. We found that the spatiotemporal feature added to the model serves as a regularizing tool that enables a precise reconstruction of the original solution.

Related Topics

Soliton

Fourier Transform

Partial Differential Equation

Mathematical Analysis

Physics

Mathematics

Differential Equation

Concepts

Dispersion (optics) Nonlinear Schrödinger equation Soliton Operator (biology) Nonlinear system Fourier transform Partial differential equation Mathematical analysis Ordinary differential equation Applied mathematics Physics Mathematics Differential equation Schrödinger equation Quantum mechanics Gene Biochemistry Transcription factor Chemistry Repressor

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Type: article
Language: en
Landing Page: https://doi.org/10.3390/sym14030465
PDF: https://www.mdpi.com/2073-8994/14/3/465/pdf?version=1645776858
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Cited By: 1
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DOI: https://doi.org/10.3390/sym14030465

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Title: Analytical and Data-Driven Wave Approximations of an Extended Schrödinger Equation

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Language: en

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Publication year: 2022

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Authors: Rachel Klauss, Aaron Phillips, José Vega-Guzmán

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Landing page: https://doi.org/10.3390/sym14030465

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Concepts: Dispersion (optics), Nonlinear Schrödinger equation, Soliton, Operator (biology), Nonlinear system, Fourier transform, Partial differential equation, Mathematical analysis, Ordinary differential equation, Applied mathematics, Physics, Mathematics, Differential equation, Schrödinger equation, Quantum mechanics, Gene, Biochemistry, Transcription factor, Chemistry, Repressor

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Cited by: 1

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