Article

**Proceedings of the International Research Program on Nonlinear PDE, H. Holden and K. H. Karlsen (eds), 151-158, Contemp. Math. 526, 2010**[DOI: 10.1090/conm/526/10380]

## On the Cauchy Problem for the modified Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data

### Iryna Egorova and Gerald Teschl

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.

** MSC2000:** Primary 35Q53, 37K15; Secondary 37K20, 81U40

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

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