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

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16 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
Journal	Letters in Mathematical Physics
Volume	96
Issue number	1-3
DOIs	https://doi.org/10.1007/s11005-010-0430-4
Publication status	Published - 2011

Keywords

74J30
37K15
65Z05
three-wave resonant interaction
spectral theory
numerical computation

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10.1007/s11005-010-0430-4

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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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AU - Conforti, Matteo

AU - Baronio, Fabio

AU - Wabnitz, Stefan

AU - Lombardo, Sara

PY - 2011

Y1 - 2011

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.

KW - 74J30

KW - 37K15

KW - 65Z05

KW - three-wave resonant interaction

KW - spectral theory

KW - numerical computation

UR - https://www.scopus.com/pages/publications/79954792532

U2 - 10.1007/s11005-010-0430-4

DO - 10.1007/s11005-010-0430-4

M3 - Article

SN - 0377-9017

VL - 96

SP - 367

EP - 403

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1-3

ER -

The three wave resonant interaction equations: spectral and numerical methods

Abstract

Keywords

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