Higher-order nonlinear dynamical systems and invariant Lagrangians on a Lie group: The case of nonlocal Hunter-Saxton type peakons

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60077344%3A_____%2F24%3A00616591" target="_blank" >RIV/60077344:_____/24:00616591 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s12346-024-01018-8" target="_blank" >https://doi.org/10.1007/s12346-024-01018-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12346-024-01018-8" target="_blank" >10.1007/s12346-024-01018-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Higher-order nonlinear dynamical systems and invariant Lagrangians on a Lie group: The case of nonlocal Hunter-Saxton type peakons

Popis výsledku v původním jazyce

A G-strand is an evolutionary map g(t,s):RxR> G into a Lie group G that follows from the Hamilton's principle for a certain class of G-invariant Lagrangians defined on the Lie algebra of the group G. t and s are independent variables associated to a G-invariant Lagrangian. The G-strand equations comprises a system of integrable partial differential equations obtained from the Euler-Poincare variational equations coupled to an auxiliary zero curvature equation. Some of these integrable partial differential equations include the Hunter-Saxton equation that arises in the study of nematic liquid crystals and the Camassa-Holm equation that arises in modeling waves in shallow water including solitons and peakons. However, nonlocal integrable systems have attracted significant attention in recent years. In this study, we use a higher-order nonlocal operator approach to study nonlocal Hunter-Saxton type peakons. Peakons-antipeakons collision on Lie group is also analyzed and discussed. It was observed that the system of 'two-peakon' collisions exhibits a kind of disordered behavior which is observed in various integrable and non-integrable nonlinear evolution dynamical systems.

Název v anglickém jazyce

Higher-order nonlinear dynamical systems and invariant Lagrangians on a Lie group: The case of nonlocal Hunter-Saxton type peakons

Popis výsledku anglicky

A G-strand is an evolutionary map g(t,s):RxR> G into a Lie group G that follows from the Hamilton's principle for a certain class of G-invariant Lagrangians defined on the Lie algebra of the group G. t and s are independent variables associated to a G-invariant Lagrangian. The G-strand equations comprises a system of integrable partial differential equations obtained from the Euler-Poincare variational equations coupled to an auxiliary zero curvature equation. Some of these integrable partial differential equations include the Hunter-Saxton equation that arises in the study of nematic liquid crystals and the Camassa-Holm equation that arises in modeling waves in shallow water including solitons and peakons. However, nonlocal integrable systems have attracted significant attention in recent years. In this study, we use a higher-order nonlocal operator approach to study nonlocal Hunter-Saxton type peakons. Peakons-antipeakons collision on Lie group is also analyzed and discussed. It was observed that the system of 'two-peakon' collisions exhibits a kind of disordered behavior which is observed in various integrable and non-integrable nonlinear evolution dynamical systems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Qualitative Theory of Dynamical Systems

ISSN

1575-5460

e-ISSN

1662-3592

Svazek periodika

23

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

24

Strana od-do

161

Kód UT WoS článku

001201824600004

EID výsledku v databázi Scopus

2-s2.0-85190240466