scholarly journals Long-time asymptotics for the Sasa–Satsuma equation via nonlinear steepest descent method

2019 ◽  
Vol 60 (1) ◽  
pp. 011504 ◽  
Author(s):  
Nan Liu ◽  
Boling Guo
Keyword(s):  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Nonlinear Steepest Descent

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 OF THE TODA LATTICE FOR DECAYING INITIAL DATA REVISITED

2009 ◽  
Vol 21 (01) ◽  
pp. 61-109 ◽  
Author(s):  
HELGE KRÜGER ◽  
GERALD TESCHL
Keyword(s):  
Initial Data ◽  
Toda Lattice ◽  
Steepest Descent ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Nonlinear Steepest Descent

The purpose of this article is to give a streamlined and self-contained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest descent.

Sign in / Sign up

Export Citation Format

Share Document