Modulated elliptic wave and asymptotic solitons in a shock problem to the modified Korteweg-de Vries equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00237412" target="_blank" >RIV/68407700:21340/15:00237412 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1088/1751-8113/48/30/305201" target="_blank" >http://dx.doi.org/10.1088/1751-8113/48/30/305201</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8113/48/30/305201" target="_blank" >10.1088/1751-8113/48/30/305201</a>

Result language

angličtina

Original language name

Modulated elliptic wave and asymptotic solitons in a shock problem to the modified Korteweg-de Vries equation

Original language description

We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg-de Vries equation with an initial function of the step type. This function rapidly tends to zero as x -> +infinity and to some positive constant c as x -> -infinity. In 1989 Khruslov and Kotlyarov have found (Khruslov and Kotlyarov 1989 Inverse Problems 5 1075-88) that for a large time the solution breaks up into a train of asymptotic solitons located in the domain 4c(2)t - C-N ln t < x <= 4c(2)t (C-N is a constant). The number N of these solitons grows unboundedly as t -> infinity. In 2010 Kotlyarov and Minakov have studied temporary asymptotics of the solution of the Cauchy problem on the whole line (Kotlyarov and Minakov 2010 J. Math. Phys. 51 093506) and havefound that in the domain -6c(2)t < x < 4c(2)t this solution is described by a modulated elliptic wave. We consider here the modulated elliptic wave in the domain 4c(2)t - C-N ln t < x <= 4c(2)t .

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/EE2.3.30.0034" target="_blank" >EE2.3.30.0034: Support of inter-sectoral mobility and quality enhancement of research teams at Czech Technical University in Prague</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2015

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

—

Volume of the periodical

48

Issue of the periodical within the volume

30

Country of publishing house

GB - UNITED KINGDOM

Number of pages

35

Pages from-to

1-35

UT code for WoS article

000358794100006

EID of the result in the Scopus database

2-s2.0-84937002631