Document Type

Conference Paper

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Applied mathematics

Publication Details

The article has been submitted to the proceedings of the International Conference "Physics and Mathematics of Nonlinear Phenomena", 22-29 June, 2013, Gallipoli, Italy. It will be published in a special issue of IOP Conference Series (Journal of Physics).

Abstract

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.

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