Influence of viscosity on the structure of shock waves in the MKdV model

A “non-self-adjoint” integrable MKdV model with boundary conditions of “step-like” type is considered. The time-asymptotic behavior of the solution for the Cauchy problem is obtained. A similar problem for the dissipative perturbation of this problem is discussed. Bibliography: 10 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 37–42. Translated by R. F. Bikbaev.