scholarly journals Self-similar planar curves related to modified Korteweg–de Vries equation

2007 ◽  
Vol 235 (1) ◽  
pp. 56-73 ◽  
Author(s):  
G. Perelman ◽  
L. Vega
Keyword(s):  
Vries Equation ◽  
Planar Curves ◽  
De Vries ◽  
Self Similar

scholarly journals Self-Similar Dynamics for the Modified Korteweg–de Vries Equation

2020 ◽  
Author(s):  
Simão Correia ◽  
Raphaël Côte ◽  
Luis Vega
Keyword(s):  
Vries Equation ◽  
Well Posedness ◽  
Critical Space ◽  
Asymptotic Description ◽  
De Vries ◽  
Self Similar ◽  
Similar Solutions

Abstract We prove a local well-posedness result for the modified Korteweg–de Vries equation in a critical space designed so that is contains self-similar solutions. As a consequence, we can study the flow of this equation around self-similar solutions: in particular, we give an asymptotic description of small solutions as $t \to +\infty$.

scholarly journals Near critical, self-similar, blow-up solutions of the generalised Korteweg–de Vries equation: Asymptotics and computations

2020 ◽  
Vol 401 ◽  
pp. 132179
Author(s):  
Pierluigi Amodio ◽  
Chris J. Budd ◽  
Othmar Koch ◽  
Vivi Rottschäfer ◽  
Giuseppina Settanni ◽  
...  
Keyword(s):  
Blow Up ◽  
Vries Equation ◽  
De Vries ◽  
Self Similar

Integration of the nonlinear modified Korteweg-de Vries equation with a loaded term

2020 ◽  
Vol 2020 (2) ◽  
pp. 85-98
Author(s):  
A.B. Khasanov ◽  
T.J. Allanazarova
Keyword(s):  
Vries Equation ◽  
De Vries ◽  
Loaded Term

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

scholarly journals A flux reconstruction method for the Korteweg-de Vries equation

2021 ◽  
Vol 1978 (1) ◽  
pp. 012031
Author(s):  
Ningbo Guo ◽  
Yaming Chen ◽  
Xiaogang Deng
Keyword(s):  
Vries Equation ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
De Vries
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