Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations

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.

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