Article

Letters in Mathematical Physics

, Volume 96, Issue 1, pp 367-403

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

  • Antonio DegasperisAffiliated withDipartimento di Fisica, Università di Roma “La Sapienza”Istituto Nazionale di Fisica Nucleare, Sezione di Roma
  • , Matteo ConfortiAffiliated withCNISM and Dipartimento di Ingegneria dell’Informazione, Università di Brescia Email author 
  • , Fabio BaronioAffiliated withCNISM and Dipartimento di Ingegneria dell’Informazione, Università di Brescia
  • , Stefan WabnitzAffiliated withCNISM and Dipartimento di Ingegneria dell’Informazione, Università di Brescia
  • , Sara LombardoAffiliated withDepartment of Mathematics, Vrije UniversiteitSchool of Mathematics, University of Manchester

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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.

Mathematics Subject Classification (2000)

74J30 37K15 65Z05

Keywords

three-wave resonant interaction spectral theory numerical computation