The nonlinear steepest descent method: Asymptotics for initial-boundary value problems

Abstract

We consider the rigorous derivation of asymptotic formulas for initial-boundary value problems using the nonlinear steepest descent method. We give detailed derivations of the asymptotics in the similarity and self-similar sectors for the mKdV equation in the quarter plane. Precise and uniform error estimates are presented in detail.

38 pages, minor corrections, improved presentation. arXiv admin note: text overlap with arXiv:1501.05329