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On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data. II: Perturbations with finite moments. (English) Zbl 1314.35136

Summary: We solve the Cauchy problem for the Korteweg-de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of finite derivatives with finite moments.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B15 Almost and pseudo-almost periodic solutions to PDEs
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
81U40 Inverse scattering problems in quantum theory
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