Iryna Egorova, Gerald Teschl
On the Cauchy Problem for the Modified Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data
The paper is published: in H. Holden and K. H. Karlsen (eds): 'Proceedings of the International Research Program on Nonlinear PDE' Contemp. Math. 526, Amer. Math. Soc., Providence (2010) 151-158

MSC:

34A55 Inverse problems

34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)

34L25 Scattering theory

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

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 modified Korteweg--de Vries equation with
steplike quasi-periodic, finite-gap initial conditions under the assumption
that the perturbations have a given number of derivatives and moments finite.


Keywords: mKdV, inverse scattering, finite-gap background, steplike