Iryna Egorova, Gerald Teschl
On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data II. Perturbations with Finite Moments
The paper is published: J. d'Analyse Math. 115:1 (2011) 71-101

MSC:

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07}

34A55 Inverse problems

34L99 None of the above but in this section

58F07 Completely integrable systems (including systems with an infinite number of degrees of freedom)

14H99 None of the above but in this section

81U40 Inverse scattering problems, See also {58F07, 58F19}

Abstract: 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 derivatives with finite moments.
Keywords: KdV, inverse scattering, finite-gap background, steplike
Notes: second and final version