The nonlinear steepest descent method: Asymptotics for initial-boundary value problems
Jonatan Lenells
TL;DR
This paper rigorously derives asymptotic formulas for initial-boundary value problems of the mKdV equation using the nonlinear steepest descent method, providing detailed derivations and error estimates in specific sectors.
Contribution
It introduces a detailed, rigorous application of the nonlinear steepest descent method to initial-boundary value problems, including precise error estimates.
Findings
Asymptotic formulas for mKdV in quarter plane derived
Uniform error estimates established
Asymptotics in similarity and self-similar sectors detailed
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.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Numerical methods for differential equations · Advanced Numerical Methods in Computational Mathematics