Geodesic
Initial-Boundary Value Problems for Linear and Soliton PDEs
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 184-201

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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.
Mots-clés : solitons
Keywords: integrability, boundary conditions. 
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     author = {A. Degasperis and S. V. Manakov and P. M. Santini},
     title = {Initial-Boundary {Value} {Problems} for {Linear} and {Soliton} {PDEs}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {184--201},
     publisher = {mathdoc},
     volume = {133},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a4/}
}
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A. Degasperis; S. V. Manakov; P. M. Santini. Initial-Boundary Value Problems for Linear and Soliton PDEs. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 184-201. http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a4/