Letters in Mathematical Physics

, Volume 96, Issue 1, pp 367–403

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

  • Antonio Degasperis
  • Matteo Conforti
  • Fabio Baronio
  • Stefan Wabnitz
  • Sara Lombardo
Article

DOI: 10.1007/s11005-010-0430-4

Cite this article as:
Degasperis, A., Conforti, M., Baronio, F. et al. Lett Math Phys (2011) 96: 367. doi:10.1007/s11005-010-0430-4

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)

74J3037K1565Z05

Keywords

three-wave resonant interactionspectral theorynumerical computation

Copyright information

© Springer 2010

Authors and Affiliations

  • Antonio Degasperis
    • 2
    • 3
  • Matteo Conforti
    • 1
  • Fabio Baronio
    • 1
  • Stefan Wabnitz
    • 1
  • Sara Lombardo
    • 4
    • 5
  1. 1.CNISM and Dipartimento di Ingegneria dell’InformazioneUniversità di BresciaBresciaItaly
  2. 2.Dipartimento di FisicaUniversità di Roma “La Sapienza”RomeItaly
  3. 3.Istituto Nazionale di Fisica NucleareSezione di RomaRomeItaly
  4. 4.Department of MathematicsVrije UniversiteitAmsterdamThe Netherlands
  5. 5.School of MathematicsUniversity of ManchesterManchesterUK