Soliton resolution and asymptotic stability of \(N\)-soliton solutions for the defocusing mKdV equation with finite density type initial data

Soliton resolution and asymptotic stability of \(N\)-soliton solutions for the defocusing mKdV equation with finite density type initial data

We consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with finite density type initial data. With the \(\bar{\partial}\) generalization of the nonlinear steepest descent method of Deift and Zhou, we extrapolate the leading order approximation to the solution of...

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Veröffentlicht in:arXiv.org 2021-08
Hauptverfasser: Zhang, Zechuan, Xu, Taiyang, Fan, Engui
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Cauchy problems
Defocusing
Density
Solitary waves
Stability
Steepest descent method
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Zusammenfassung:We consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with finite density type initial data. With the \(\bar{\partial}\) generalization of the nonlinear steepest descent method of Deift and Zhou, we extrapolate the leading order approximation to the solution of mKdV for large time in the solitonic space-time region \(|x/t+4|
ISSN:2331-8422