Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475579" target="_blank" >RIV/00216208:11320/23:10475579 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=E4a6iCCrss" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=E4a6iCCrss</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/cpa.22106" target="_blank" >10.1002/cpa.22106</a>
Alternative languages
Result language
angličtina
Original language name
Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation
Original language description
We analyse the case of a dense modified Korteweg-de Vries (mKdV) soliton gas and its large time behaviour in the presence of a single trial soliton. We show that the solution can be expressed in terms of Fredholm determinants as well as in terms of a Riemann-Hilbert problem. We then show that the solution can be decomposed as the sum of the background gas solution (a modulated elliptic wave), plus a soliton solution: the individual expressions are however quite convoluted due to the interaction dynamics. Additionally, we are able to derive the local phase shift of the gas after the passage of the soliton, and we can trace the location of the soliton peak as the dynamics evolves. Finally, we show that the soliton peak, while interacting with the soliton gas, has an oscillatory velocity whose leading order average value satisfies the kinetic velocity equation analogous to the one posited by V. Zakharov and G. El.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications on pure and applied mathematics
ISSN
0010-3640
e-ISSN
1097-0312
Volume of the periodical
76
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
67
Pages from-to
3233-3299
UT code for WoS article
001014596900001
EID of the result in the Scopus database
2-s2.0-85161304835