Iryna Egorova, Katrin Grunert, and Gerald Teschl
On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwarz-Type Perturbations
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ABSTRACT.  We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the mutual spectral bands either coincide or are disjoint.