Nonlinearity 22, 1431-1457 (2009) [DOI: 10.1088/0951-7715/22/6/009]

On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations

Iryna Egorova, Katrin Grunert, and Gerald Teschl

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 respective spectral bands either coincide or are disjoint.

MSC2000: Primary 35Q53, 37K15; Secondary 37K20, 81U40
Keywords: KdV, inverse scattering, finite-gap background, steplike

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