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

Year: 2011

Authors: Degasperis A., Conforti M., Baronio F., Wabnitz S., Lombardo S.

Autors Affiliation: CNISM and Dipartimento di Ingegneria dell\’Informazione, Università di Brescia, Brescia, Italy; Dipartimento di Fisica, Università di Roma La Sapienza, Rome, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome, Italy; Department of Mathematics, Vrije Universiteit, Amsterdam, Netherlands; School of Mathematics, University of Manchester, Alan Turing Building, Manchester, United Kingdom

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.

Journal/Review: LETTERS IN MATHEMATICAL PHYSICS

Volume: 96 (1-3)      Pages from: 367  to: 403

KeyWords: numerical computation; spectral theory; three-wave resonant interaction
DOI: 10.1007/s11005-010-0430-4

Citations: 13
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