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

Antonio Degasperis (1) , Matteo Conforti (2) , Fabio Baronio (2) , Stefan Wabnitz (2) , Sara Lombardo (3, 4)

1 INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]
2 Dipartimento di Ingegneria dell'Informazione [Brescia]
3 School of Mathematics - Department of Mathematics [Manchester]
4 VU - Vrije Universiteit Amsterdam [Amsterdam]

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 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.

Domaines: Systèmes Solubles et Intégrables [nlin.SI]; Formation de Structures et Solitons [nlin.PS]

Antonio Degasperis, Matteo Conforti, Fabio Baronio, Stefan Wabnitz, Sara Lombardo. The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods. Letters in Mathematical Physics, 2011, 96 (1-3), pp.367-403. ⟨10.1007/s11005-010-0430-4⟩. ⟨hal-02395151⟩