Shock waves in the modified Korteweg-de Vries-Burgers equation

摘要

The asymptotics ast→ + ∞ of shock waves of the modified Korteweg-de Vries-Burgers (MKdV-B) equation is investigated. An attractor interpretation of shock problems for integrable systems is presented and some problems of nonlinear stability are discussed. The MKdV-B equation is considered as a nonconservative perturbation of the integrable modified Korteweg-de Vries (MKdV) equation. The MKdV equation considered here has anon-self-adjointLax pair. In spite of this difficulty, acomplexWhitham deformation is construc