The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

Antonio Degasperis; Matteo Conforti; Fabio Baronio; Stefan Wabnitz; Sara Lombardo

doi:10.1007/s11005-010-0430-4

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

Antonio Degasperis, Matteo Conforti^*, Fabio Baronio, Stefan Wabnitz, Sara Lombardo

^*Corresponding author for this work

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.

Original language	English
Pages (from-to)	367-403
Number of pages	37
Journal	Letters in Mathematical Physics
Volume	96
Issue number	1-3
DOIs	https://doi.org/10.1007/s11005-010-0430-4
Publication status	Published - Jun 2011

Keywords

numerical computation
spectral theory
three-wave resonant interaction

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-010-0430-4

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title = "The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods",

abstract = "The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.",

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author = "Antonio Degasperis and Matteo Conforti and Fabio Baronio and Stefan Wabnitz and Sara Lombardo",

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AU - Baronio, Fabio

AU - Wabnitz, Stefan

AU - Lombardo, Sara

PY - 2011/6

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N2 - The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.

AB - The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.

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KW - spectral theory

KW - three-wave resonant interaction

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The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

Abstract

Keywords

ASJC Scopus subject areas

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