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

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 respective spectral bands either coincide or are disjoint.

29 pages

References in corpus (2)

• Stability of Periodic Soliton Equations under Short Range Perturbations
• Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials

Cited by in corpus (3)

• Shock problem for MKdV equation: Long time Dynamics of the Step-like initial data
• Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds
• The Transformation Operator for One-Dimensional Schroedinger Operators on Almost Periodic Infinite-Gap Backgrounds