Initial-Boundary Value Problems for Linear and Soliton PDEs

2002/05/14 by A. Degasperis, S. V. Manakov, Degasperis, A. +4
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0205030

18 pages, LATEX, submitted to the proccedings of NEEDS 2001 - Special Issue, to be published in the Journal of Theoretical and Mathematical Physics

arxiv created 2002/05/14 · arxiv updated 2009/11/30

Abstract

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.

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