scholarly journals Self-similar solutions and critical spaces for the modified Korteweg-de Vries equation

2018 ◽  
pp. 1-15
Author(s):  
Raphaël Côte
Keyword(s):  
Vries Equation ◽  
Critical Spaces ◽  
De Vries ◽  
Self Similar ◽  
Similar Solutions

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
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