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Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations. (English) Zbl 1230.30026

Summary: It is suggested here that an interesting and important line of inquiry is the elaboration of methods of inverse scattering transform (IST) type in contexts where non-homogeneous boundary conditions intercede. The issue, which has practical relevance we indicate by example, appears ripe for development, thanks to recent new ideas interjected into the panoply of IST methodologies. A sketch of the principal steps envisaged in carrying out analysis of boundary-value problems using inverse scattering ideas is provided.

MSC:

30E25 Boundary value problems in the complex plane
35Q53 KdV equations (Korteweg-de Vries equations)
35Q15 Riemann-Hilbert problems in context of PDEs
35Q35 PDEs in connection with fluid mechanics
35Q51 Soliton equations
35P25 Scattering theory for PDEs
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