scholarly journals On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves

2017 ◽  
Vol 13 (4) ◽  
pp. 325-343
Author(s):  
K. Andreiev ◽  
◽  
I. Egorova ◽  
Keyword(s):  
Initial Data ◽  
Vries Equation ◽  
Rarefaction Waves ◽  
Time Asymptotics ◽  
De Vries ◽  
Long Time ◽  
Long Time Asymptotics

scholarly journals Long-time asymptotics for the Korteweg–de Vries equation with step-like initial data

Nonlinearity ◽  
2013 ◽  
Vol 26 (7) ◽  
pp. 1839-1864 ◽  
Author(s):  
Iryna Egorova ◽  
Zoya Gladka ◽  
Volodymyr Kotlyarov ◽  
Gerald Teschl
Keyword(s):  
Initial Data ◽  
Vries Equation ◽  
Time Asymptotics ◽  
De Vries ◽  
Long Time ◽  
Long Time Asymptotics

Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg—de Vries equation

2011 ◽  
Vol 141 (2) ◽  
pp. 287-317 ◽  
Author(s):  
Yvan Martel ◽  
Frank Merle
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
Time Asymptotics ◽  
The Kdv Equation ◽  
De Vries ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Different Sources ◽  
Integrability Theory

We review recent nonlinear partial differential equation techniques developed to address questions concerning solitons for the quartic generalized Korteweg—de Vries equation (gKdV) and other generalizations of the KdV equation. We draw a comparison between results obtained in this way and some elements of the classical integrability theory for the original KdV equation, which serve as a reference for soliton and multi-soliton problems. First, known results on stability and asymptotic stability of solitons for gKdV equations are reviewed from several different sources. Second, we consider the problem of the interaction of two solitons for the quartic gKdV equation. We focus on recent results and techniques from a previous paper by the present authors concerning the interaction of two almost-equal solitons.

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