This article is cited in 25 papers

Initial-Boundary Value Problems for Linear and Soliton PDEs

A. Degasperis^a, S. V. Manakov^b, P. M. Santini<sup>a

a</sup> University of Rome "La Sapienza"
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: 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.

Keywords: solitons, integrability, boundary conditions.

DOI: 10.4213/tmf389

 English version: Theoretical and Mathematical Physics, 2002, 133:2, 1475–1489

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