RUS  ENG ЖУРНАЛЫ   ПЕРСОНАЛИИ   ОРГАНИЗАЦИИ   КОНФЕРЕНЦИИ   СЕМИНАРЫ   ВИДЕОТЕКА   ПАКЕТ AMSBIB
Общая информация
Последний выпуск
Архив
Импакт-фактор

Поиск публикаций
Поиск ссылок

RSS
Последний выпуск
Текущие выпуски
Архивные выпуски
Что такое RSS



SIGMA:
Год:
Том:
Выпуск:
Страница:
Найти






Персональный вход:
Логин:
Пароль:
Запомнить пароль
Войти
Забыли пароль?
Регистрация


SIGMA, 2006, том 2, 044, 18 страниц (Mi sigma72)  

Эта публикация цитируется в 30 научных статьях (всего в 30 статьях)

Hamiltonian Flows of Curves in $G/SO(N)$ and Vector Soliton Equations of mKdV and Sine-Gordon Type

Stephen C. Anco

Department of Mathematics, Brock University, Canada

Аннотация: The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of non-stretching curves in Riemannian symmetric spaces $G/SO(N)$. These spaces are exhausted by the Lie groups $G=SO(N+1),SU(N)$. The derivation of the bi-Hamiltonian structure uses a parallel frame and connection along the curve, tied to a zero curvature Maurer–Cartan form on $G$, and this yields the mKdV recursion operators in a geometric vectorial form. The kernel of these recursion operators is shown to yield two hyperbolic vector generalizations of the sine-Gordon equation. The corresponding geometric curve flows in the hierarchies are described in an explicit form, given by wave map equations and mKdV analogs of Schrödinger map equations.

Ключевые слова: bi-Hamiltonian; soliton equation; recursion operator; symmetric space; curve flow; wave map; Schrödinger map; mKdV map

DOI: https://doi.org/10.3842/SIGMA.2006.044

Полный текст: PDF файл (294 kB)
Полный текст: http://emis.mi.ras.ru/.../Paper044
Список литературы: PDF файл   HTML файл

Реферативные базы данных:

ArXiv: nlin.SI/0512046
Тип публикации: Статья
MSC: 37K05; 37K10; 37K25; 35Q53; 53C35
Поступила: 12 декабря 2005 г.; в окончательном варианте 12 апреля 2006 г.; опубликована 19 апреля 2006 г.
Язык публикации: английский

Образец цитирования: Stephen C. Anco, “Hamiltonian Flows of Curves in $G/SO(N)$ and Vector Soliton Equations of mKdV and Sine-Gordon Type”, SIGMA, 2 (2006), 044, 18 pp.

Цитирование в формате AMSBIB
\RBibitem{Anc06}
\by Stephen C.~Anco
\paper Hamiltonian Flows of Curves in $G/SO(N)$ and Vector Soliton Equations of mKdV and Sine-Gordon Type
\jour SIGMA
\yr 2006
\vol 2
\papernumber 044
\totalpages 18
\mathnet{http://mi.mathnet.ru/sigma72}
\crossref{https://doi.org/10.3842/SIGMA.2006.044}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2217753}
\zmath{https://zbmath.org/?q=an:1102.37042}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000207065100043}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889235405}


Образцы ссылок на эту страницу:
  • http://mi.mathnet.ru/sigma72
  • http://mi.mathnet.ru/rus/sigma/v2/p44

    ОТПРАВИТЬ: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Wo, WF, “Integrable motions of curves in S(1)xR”, Journal of Geometry and Physics, 57:8 (2007), 1733  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Changzheng Qu, Yanyan Li, “Deformation of Surfaces Induced by Motions of Curves in Higherdimensional Similarity Geometries”, Methods and Applications of Analysis, 14:3 (2007), 273–286  crossref  mathscinet
    3. Gloria Marí Beffa, “Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems”, SIGMA, 4 (2008), 034, 23 pp.  mathnet  crossref  mathscinet  zmath
    4. Qu, CZ, “Higher-Dimensional Integrable Systems Arising from Motions of Curves on S-2(R) and S-3(R)”, Communications in Theoretical Physics, 50:4 (2008), 841  crossref  mathscinet  adsnasa  isi  scopus
    5. Li, YY, “Higher-dimensional integrable systems induced by motions of curves in affine geometries”, Chinese Physics Letters, 25:6 (2008), 1931  crossref  adsnasa  isi  elib  scopus
    6. Anco, SC, “Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces”, Journal of Geometry and Physics, 58:1 (2008), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Anco S.C., “Hamiltonian Curve Flows in Lie Groups G Subset of U(N) and Vector NLS, Mkdv, sine-Gordon Soliton Equations”, Symmetries and Overdetermined Systems of Partial Differential Equations, IMA Volumes in Mathematics and its Applications, 144, eds. Eastwood M., Miller W., Springer, 2008, 223–250  crossref  mathscinet  zmath  isi
    8. Beffa G.M., “Projective-Type Differential Invariants for Curves and their Associated PDEs of KdV Type”, Symmetries and Overdetermined Systems of Partial Differential Equations, IMA Volumes in Mathematics and its Applications, 144, eds. Eastwood M., Miller W., Springer, 2008, 265–275  crossref  mathscinet  zmath  isi
    9. Wang, JP, “Lenard scheme for two-dimensional periodic Volterra chain”, Journal of Mathematical Physics, 50:2 (2009), 023506  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. Beffa, GM, “Hamiltonian evolution of curves in classical affine geometries”, Physica D-Nonlinear Phenomena, 238:1 (2009), 100  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Anco S.C., Asadi E., “Quaternionic soliton equations from Hamiltonian curve flows in HPn”, Journal of Physics A-Mathematical and Theoretical, 42:48 (2009), 485201  crossref  mathscinet  zmath  isi  scopus
    12. Anco S.C., Vacaru S.I., “Curve flows in Lagrange-Finsler geometry, bi-Hamiltonian structures and solitons”, Journal of Geometry and Physics, 59:1 (2009), 79–103  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Vacaru S.I., “Curve Flows and Solitonic Hierarchies Generated by Einstein Metrics”, Acta Applicandae Mathematicae, 110:1 (2010), 73–107  crossref  mathscinet  zmath  isi  elib  scopus
    14. Anco S.C., Myrzakulov R., “Integrable generalizations of Schrodinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces”, J Geom Phys, 60:10 (2010), 1576–1603  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. Beffa G.M., “Bi-Hamiltonian flows and their realizations as curves in real semisimple homogeneous manifolds”, Pacific J. Math., 247:1 (2010), 163–188  crossref  zmath  isi  scopus
    16. Li Ya., Qu Ch., Shu Sh., “Integrable motions of curves in projective geometries”, J Geom Phys, 60:6–8 (2010), 972–985  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. Mikhailov A., “Bihamiltonian Structure of the Classical Superstring in AdS(5) X S-5”, Adv. Theor. Math. Phys., 14:6 (2010), 1585–1620  crossref  mathscinet  isi  elib  scopus
    18. Beffa G.M., “Moving Frames, Geometric Poisson Brackets and the KdV-Schwarzian Evolution of Pure Spinors”, Ann. Inst. Fourier, 61:6 (2011), 2405–2434  crossref  mathscinet  zmath  isi  scopus
    19. Song J., Qu Ch., “Integrable systems and invariant curve flows in centro-equiaffine symplectic geometry”, Physica D-Nonlinear Phenomena, 241:4 (2012), 393–402  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    20. Anco S.C., Asadi E., “Symplectically Invariant Soliton Equations From Non-Stretching Geometric Curve Flows”, J. Phys. A-Math. Theor., 45:47 (2012), 475207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    21. Eastwood M., Beffa G.M., “Geometric Poisson Brackets on Grassmannians and Conformal Spheres”, Proc. R. Soc. Edinb. Sect. A-Math., 142:3 (2012), 525–561  crossref  mathscinet  zmath  isi  elib  scopus
    22. Changzheng Qu, Junfeng Song, Ruoxia Yao, “Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries”, SIGMA, 9 (2013), 001, 19 pp.  mathnet  crossref  mathscinet
    23. Atsushi Fujioka, Takashi Kurose, “Multi-Hamiltonian Structures on Spaces of Closed Equicentroaffine Plane Curves Associated to Higher KdV Flows”, SIGMA, 10 (2014), 048, 11 pp.  mathnet  crossref  mathscinet
    24. Igonin S., Marvan M., “on Construction of Symmetries and Recursion Operators From Zero-Curvature Representations and the Darboux-Egoroff System”, J. Geom. Phys., 85 (2014), 106–123  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    25. Qu Ch., Han J., Kang J., “Backlund Transformations For Integrable Geometric Curve Flows”, Symmetry-Basel, 7:3 (2015), 1376–1394  crossref  mathscinet  zmath  isi  scopus
    26. Li YanYan, Qu ChangZheng, “Symplectic Invariants For Curves and Integrable Systems in Similarity Symplectic Geometry”, Sci. China-Math., 58:7 (2015), 1415–1432  crossref  mathscinet  zmath  isi  scopus
    27. Mikhailov A.V., Papamikos G., Wang J.P., “Dressing method for the vector sine-Gordon equation and its soliton interactions”, Physica D, 325 (2016), 53–62  crossref  mathscinet  zmath  isi  scopus
    28. Alkan K., Anco S.C., “Integrable systems from inelastic curve flows in 2? and 3? dimensional Minkowski space”, J. Nonlinear Math. Phys., 23:2 (2016), 256–299  crossref  mathscinet  isi  elib  scopus
    29. Song J., Qu Ch., Yao R., “Integrable systems and invariant curve flows in symplectic Grassmannian space”, Physica D, 349 (2017), 1–11  crossref  mathscinet  zmath  isi  scopus
    30. Ahmed A., Anco S.C., Asadi E., “Unitarily-Invariant Integrable Systems and Geometric Curve Flows in Su (N+1)/U(N) and So(2N)/U(N)”, J. Phys. A-Math. Theor., 51:6 (2018), 065205  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Просмотров:
    Эта страница:347
    Полный текст:43
    Литература:30
     
    Обратная связь:
     Пользовательское соглашение  Регистрация  Логотипы © Математический институт им. В. А. Стеклова РАН, 2019