Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Communications on pure and applied mathematics

ISSN

0010-3640

e-ISSN

1097-0312

Svazek periodika

76

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

67

Strana od-do

3233-3299

Kód UT WoS článku

001014596900001

EID výsledku v databázi Scopus

2-s2.0-85161304835