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The matrix KdV equation with a negative dispersion term is considered in the right upper
quarter–plane. The evolution law is derived for the Weyl function of a corresponding
auxiliary linear system. Using the low energy asymptotics of the Weyl functions, the
unboundedness of solutions is obtained for some classes of the initial–boundary
conditions.
A general theorem on the GBDT version of the Bäcklund-Darboux transformation for systems
depending rationally on the spectral parameter is treated and its applications to
nonlinear equations are given. Explicit solutions of direct and inverse problems for
Dirac-type systems, including systems with singularities, and for the system auxiliary to
the -wave equation are reviewed. New results on explicit construction of
the wave functions for radial Dirac...
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