Higher-order nonlinear dynamical systems and invariant Lagrangians on a Lie group: The case of nonlocal Hunter-Saxton type peakons
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Higher-order nonlinear dynamical systems and invariant Lagrangians on a Lie group: The case of nonlocal Hunter-Saxton type peakons
Original language description
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.
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
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Qualitative Theory of Dynamical Systems
ISSN
1575-5460
e-ISSN
1662-3592
Volume of the periodical
23
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
24
Pages from-to
161
UT code for WoS article
001201824600004
EID of the result in the Scopus database
2-s2.0-85190240466