Small dispersion limit of the Korteweg–de Vries equation with periodic initial conditions and analytical description of the Zabusky–Kruskal experiment

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2016.03.003 ◽

2016 ◽

Vol 333 ◽

pp. 137-147 ◽

Author(s):

Guo Deng ◽

Gino Biondini ◽

Stefano Trillo

Keyword(s):

Vries Equation ◽

Initial Conditions ◽

Analytical Description ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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The Small Dispersion Limit of the Korteweg-De Vries Equation

Mathematical Sciences Research Institute Publications - Wave Motion: Theory, Modelling, and Computation ◽

10.1007/978-1-4613-9583-6_12 ◽

1987 ◽

pp. 295-336

Author(s):

Stephanos Venakides

Keyword(s):

Vries Equation ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.20277 ◽

2009 ◽

Vol 63 (2) ◽

pp. 203-232 ◽

Author(s):

Tom Claeys ◽

Tamara Grava

Keyword(s):

Vries Equation ◽

Leading Edge ◽

De Vries ◽

Painlevé Ii ◽

Oscillatory Zone ◽

Small Dispersion ◽

Dispersion Limit

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Solitonic Asymptotics for the Korteweg–de Vries Equation in the Small Dispersion Limit

SIAM Journal on Mathematical Analysis ◽

10.1137/090779103 ◽

2010 ◽

Vol 42 (5) ◽

pp. 2132-2154 ◽

Author(s):

Tom Claeys ◽

Tamara Grava

Keyword(s):

Vries Equation ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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The small dispersion limit of the Korteweg-de Vries equation. I

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160360302 ◽

1983 ◽

Vol 36 (3) ◽

pp. 253-290 ◽

Author(s):

Peter D. Lax ◽

C. David Levermore

Keyword(s):

Vries Equation ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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The small dispersion limit of the Korteweg-de Vries equation. III

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160360606 ◽

1983 ◽

Vol 36 (6) ◽

pp. 809-829 ◽

Author(s):

Peter D. Lax ◽

C. David Levermore

Keyword(s):

Vries Equation ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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Analysis of the small dispersion limit of a non-integrable generalized Korteweg–de Vries equation

Physica Scripta ◽

10.1088/0031-8949/88/02/025006 ◽

2013 ◽

Vol 88 (2) ◽

pp. 025006 ◽

Author(s):

Gholam-Ali Zakeri ◽

Emmanuel Yomba

Keyword(s):

Vries Equation ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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The small dispersion limit of the korteweg-de vries equation. ii

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160360503 ◽

1983 ◽

Vol 36 (5) ◽

pp. 571-593 ◽

Author(s):

Peter D. Lax ◽

C. David Levermore

Keyword(s):

Vries Equation ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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A numerical study of the small dispersion limit of the Korteweg–de Vries equation and asymptotic solutions

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2012.04.001 ◽

2012 ◽

Vol 241 (23-24) ◽

pp. 2246-2264 ◽

Author(s):

T. Grava ◽

C. Klein

Keyword(s):

Vries Equation ◽

Numerical Study ◽

Asymptotic Solutions ◽

De Vries ◽

Small Dispersion ◽

Dispersion Limit

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The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160380202 ◽

1985 ◽

Vol 38 (2) ◽

pp. 125-155 ◽

Author(s):

Stephanos Venakides

Keyword(s):

Reflection Coefficient ◽

Vries Equation ◽

De Vries ◽

Dispersion Limit

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Initial conditions for the cylindrical Korteweg‐de Vries equation

Studies in Applied Mathematics ◽

10.1111/sapm.12272 ◽

2019 ◽

Vol 143 (2) ◽

pp. 176-191 ◽

Author(s):

Roger Grimshaw

Keyword(s):

Vries Equation ◽

Initial Conditions ◽

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