Iryna Egorova and Gerald Teschl
On the Cauchy Problem for the modified Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data
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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.