Theoretical and Mathematical Physics

, Volume 133, Issue 2, pp 1475–1489

Initial-Boundary Value Problems for Linear and Soliton PDEs

  • A. Degasperis
  • S. V. Manakov
  • P. M. Santini

DOI: 10.1023/A:1021138525261

Cite this article as:
Degasperis, A., Manakov, S.V. & Santini, P.M. Theoretical and Mathematical Physics (2002) 133: 1475. doi:10.1023/A:1021138525261


We consider evolution PDEs for dispersive waves in both linear and nonlinear integrable cases and formulate the associated initial-boundary value problems in the spectral space. We propose a solution method based on eliminating the unknown boundary values by proper restrictions of the functional space and of the spectral variable complex domain. Illustrative examples include the linear Schrödinger equation on compact and semicompact n-dimensional domains and the nonlinear Schrödinger equation on the semiline.

solitons integrability boundary conditions 

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. Degasperis
  • S. V. Manakov
    • 1
  • P. M. Santini
    • 2
    • 3
  1. 1.Landau Institute for Theoretical PhysicsRAS, MoscowRussia
  2. 2.Dipartimento di FisicaUniversitá degli Studi di Roma “La Sapienza,”RomeItaly
  3. 3.Sezione di Roma, Istituto Nazionale di Fisica NucleareRomeItaly

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