The Riemann–Hilbert problem and long-time asymptotics for the Kundu–Eckhaus equation with decaying initial value

2018 ◽  
Vol 76 ◽  
pp. 81-89 ◽  
Author(s):  
Qiaozhen Zhu ◽  
Jian Xu ◽  
Engui Fan
Keyword(s):  
Hilbert Problem ◽  
Initial Value ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Riemann Hilbert Problem

scholarly journals Long-Time Asymptotics of a Three-Component Coupled mKdV System

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 573 ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Hilbert Problem ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Matrix Spectral Problem ◽  
Riemann Hilbert Problem ◽  
Nonlinear Steepest Descent

We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based on the corresponding oscillatory Riemann-Hilbert problem, the leading asympototics of the three-component mKdV system is then evaluated by using the nonlinear steepest descent method.

scholarly journals Long-time asymptotics for evolutionary crystal dislocation models

2020 ◽  
Vol 371 ◽  
pp. 107242 ◽  
Author(s):  
Matteo Cozzi ◽  
Juan Dávila ◽  
Manuel del Pino
Keyword(s):  
Time Asymptotics ◽  
Dislocation Models ◽  
Long Time ◽  
Long Time Asymptotics
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