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Auteurs principaux:	Banks, J. W., Shatah, J.
Format:	Preprint
Publié:	2025
Sujets:	Numerical Analysis
Accès en ligne:	https://arxiv.org/abs/2509.03432
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author	Banks, J. W. Shatah, J.
author_facet	Banks, J. W. Shatah, J.
contents	Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to WKEs. This new method relies on a piecewise polynomial approximation of the resonant manifold, followed by numerical quadrature of the collision integral. The approach is general in nature, and is discussed in detail here for a particular nonlinear Schrodinger model in 2 spatial dimensions. Detailed convergence studies demonstrate 2nd-order accuracy for model collision integrals, and self-convergence studies for the WKE show near 2nd-order rates. Furthermore, comparison of the WKE approximation to ensemble averages of the NLS illustrate the efficacy of the method and the validity of the WKE, for both isotropic and an-isotropic solutions.
format	Preprint
id	arxiv_https___arxiv_org_abs_2509_03432
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	A New Approach to Direct Discretization of Wave Kinetic Equations with Application to a Nonlinear Schrodinger System in 2D Banks, J. W. Shatah, J. Numerical Analysis Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to WKEs. This new method relies on a piecewise polynomial approximation of the resonant manifold, followed by numerical quadrature of the collision integral. The approach is general in nature, and is discussed in detail here for a particular nonlinear Schrodinger model in 2 spatial dimensions. Detailed convergence studies demonstrate 2nd-order accuracy for model collision integrals, and self-convergence studies for the WKE show near 2nd-order rates. Furthermore, comparison of the WKE approximation to ensemble averages of the NLS illustrate the efficacy of the method and the validity of the WKE, for both isotropic and an-isotropic solutions.
title	A New Approach to Direct Discretization of Wave Kinetic Equations with Application to a Nonlinear Schrodinger System in 2D
topic	Numerical Analysis
url	https://arxiv.org/abs/2509.03432

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