Evolution PDEs for dispersive waves are considered in both linear and
nonlinear integrable cases, and initial-boundary value problems associated with
them are formulated in spectral space. A method of solution is presented, which
is based on the elimination of the unknown boundary values by proper
restrictions of the functional space and of the spectral variable complex
domain. Illustrative examples include the linear Schroedinger equation on
compact and semicompact n-dimensional domains and the nonlinear Schroedinger
equation on the semiline.Comment: 18 pages, LATEX, submitted to the proccedings of NEEDS 2001 - Special
Issue, to be published in the Journal of Theoretical and Mathematical Physic
