Relevant bibliographies by topics / Bihamiltonian

Academic literature on the topic 'Bihamiltonian'

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Published: 10 March 2023

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Journal articles on the topic "Bihamiltonian"

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GUHA, PARTHA. "BIDIFFERENTIAL CALCULI, BICOMPLEX STRUCTURE AND ITS APPLICATION TO BIHAMILTONIAN SYSTEMS." International Journal of Geometric Methods in Modern Physics 03, no. 02 (March 2006): 209–32. http://dx.doi.org/10.1142/s0219887806001120.

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In this exposition, we study the relationship between the bihamiltonian formalism of completely integrable systems using the bidifferential calculi introduced by Dimakis and Müller-Hoissen in [1] and the bihamiltonian formulation of integrable systems with a finite number of degrees of freedom via the Frölicher–Nijenhuis geometry. This pair of bidifferetial operators are used to construct alternative Lie algebroids as shown by Camacaro and Carinena. We find its connection to Finsler geometry. We also find the dispersionless integrable hierarchies using the bidifferential ideals. Finally, we lay out its connection to Gelfand–Zakharevich bihamiltonian geometry.
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Odesskii, A. "Bihamiltonian Elliptic Structures." Moscow Mathematical Journal 4, no. 4 (2004): 941–46. http://dx.doi.org/10.17323/1609-4514-2004-4-4-941-946.

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FIGUEROA-O'FARRILL, JOSÉ M., EDUARDO RAMOS, and JAVIER MAS. "INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKDV HIERARCHIES." Reviews in Mathematical Physics 03, no. 04 (December 1991): 479–501. http://dx.doi.org/10.1142/s0129055x91000175.

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We study reductions of the even order SKP hierarchy. We prove that these systems are integrable and bihamiltonian. We derive an infinite set of independent polynomial conservation laws, prove their nontriviality, and derive Lenard relations between them. A further reduction of the simplest such hierarchy is identified with the supersymmetric KdV hierarchy of Manin and Radul. We prove that it inherits all the bihamiltonian and integrability properties from the unreduced hierarchy.
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Casati, Paolo, Gregorio Falqui, Franco Magri, and Marco Pedroni. "Bihamiltonian reductions and ωn-algebras." Journal of Geometry and Physics 26, no. 3-4 (July 1998): 291–310. http://dx.doi.org/10.1016/s0393-0440(97)00060-0.

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Ibort, A., F. Magri, and G. Marmo. "Bihamiltonian structures and Stäckel separability." Journal of Geometry and Physics 33, no. 3-4 (April 2000): 210–28. http://dx.doi.org/10.1016/s0393-0440(99)00051-0.

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Carlet, Guido, Hessel Posthuma, and Sergey Shadrin. "Bihamiltonian Cohomology of KdV Brackets." Communications in Mathematical Physics 341, no. 3 (January 2, 2016): 805–19. http://dx.doi.org/10.1007/s00220-015-2540-4.

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Casati, Paolo, and Giovanni Ortenzi. "Bihamiltonian Equations on Polynomial Virasoro Algebras." Journal of Nonlinear Mathematical Physics 13, no. 3 (January 2006): 352–64. http://dx.doi.org/10.2991/jnmp.2006.13.3.3.

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Marmo, G., A. Simoni, and F. Ventriglia. "BiHamiltonian quantum systems and Weyl quantization." Reports on Mathematical Physics 48, no. 1-2 (August 2001): 149–57. http://dx.doi.org/10.1016/s0034-4877(01)80074-4.

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Gelfand, Israel M., and Ilya Zakharevich. "Webs, Veronese curves, and bihamiltonian systems." Journal of Functional Analysis 99, no. 1 (July 1991): 150–78. http://dx.doi.org/10.1016/0022-1236(91)90057-c.

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Jodeit, Max, and Peter J. Olver. "On the equation grad f = M grad g." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 116, no. 3-4 (1990): 341–58. http://dx.doi.org/10.1017/s0308210500031541.

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SynopsisThe system of differential equations ∇f = M∇g, where M is a given square matrix, arises in many contexts. A complete solution to this problem in the case when M is a constant matrix is presented here. Applications to continuum mechanics and biHamiltonian systems are indicated.
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Dissertations / Theses on the topic "Bihamiltonian"

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Izosimov, Anton. "Singularities of bihamiltonian systems and the multidimensional rigid body." Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/9966.

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Two Poisson brackets are called compatible if any linear combination of these brackets is a Poisson bracket again. The set of non-zero linear combinations of two compatible Poisson brackets is called a Poisson pencil. A system is called bihamiltonian (with respect to a given pencil) if it is hamiltonian with respect to any bracket of the pencil. The property of being bihamiltonian is closely related to integrability. On the one hand, many integrable systems known from physics and geometry possess a bihamiltonian structure. On the other hand, if we have a bihamiltonian system, then the Casimir functions of the brackets of the pencil are commuting integrals of the system. We consider the situation when these integrals are enough for complete integrability. As it was shown by Bolsinov and Oshemkov, many properties of the system in this case can be deduced from the properties of the Poisson pencil itself, without explicit analysis of the integrals. Developing these ideas, we introduce a notion of linearization of a Poisson pencil. In terms of linearization, we give a criterion for non-degeneracy of a singular point and describe its type. These results are applied to solve the stability problem for a free multidimensional rigid body.
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Rigal, Marie-Hélène. "Géométrie globale des systèmes bihamiltoniens en dimension impaire." Montpellier 2, 1996. http://www.theses.fr/1996MON20003.

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Suivant la definition donnee par i. Gelfand et i. Zakharevitch gz, on etudie les systemes bihamiltoniens reguliers definis sur des varietes de dimension impaire 2n + 1. A un tel systeme est naturellement associe un feuilletage a de codimension n + 1, appele ame du systeme bihamiltonien. Il possede une structure transverse de tissu de veronese gz et ses feuilles sont munies d'une structure affine canonique. L'objet de la these est la description de la variete m, feuilletee par a, lorsqu'elle est fermee. Ce travail se divise en deux parties. La premiere est consacree a l'etude des feuilletages transversalement de veronese en toutes dimension et codimension et permet en particulier d'etablir que l'ame d'un systeme bihamiltonien admet un parallelisme transverse adapte a sa structure transverse et que le hamiltonien h est basique pour a. Dans la deuxieme partie, ce resultat essentiel conduit a une description assez precise, d'une part, des systemes bihamiltoniens sur les 5-varietes fermees, d'autre part, des tissus de veronese sur les 3-varietes fermees, apres en avoir effectue une etude locale prealable
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MEHDI, MOHAMAD. "Existence de lois de conservation et de systemes bihamiltoniens." Toulouse 3, 1991. http://www.theses.fr/1991TOU30049.

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Une loi de conservation sur une variete differentiable m par rapport a un champ d'endomorphisme h de tm, est une 1-forme scalaire tel que d=0 et d(h*)=0h* etant le transpose de h. Les lois de conservations ont ete introduites par lax dans l'etude de l'integrabilite des systemes differentiels et systemes bihamiltoniens. On sait en effet, d'apres les travaux de magri que le cadre geometrique des systemes completement integrables est une variete munie d'un couple de tenseurs de poisson compatibles (p,q). Les systemes completement integrables sont les champs hamiltoniens definis par les deux structures i. E. Les champs x du type x=pdh=qdk h, k deux fonctions sur m. Si par exemple p est inversible cette condition equivaut a p##1qdk=dh, ce qui signifie que dk est une loi de conservation par rapport au champ d'endomorphismes h=p##1q. Ainsi la recherche des champs completement integrables equivaut (modulo certaines conditions sur les tenseurs de poisson) a la recherche des lois de conservations. Le but de ce travail est double: 1) etudier quand un couple de tenseur de poisson compatible donne lieu, par passage au quotient a un certain feuilletage associe a un operateur de recursion h; 2) etudier l'integrabilite formelle de l'operateur differentiel qui donne les lois de conservations associees a h. Le premier probleme a ete pose par magri. On trouve une condition algebrique portant sur p et q qui assure l'existence de l'operateur h. Le deuxieme probleme a ete etudie par osborn qui a obtenu des resultats tres partiels et incomplets, sans doute a cause de la grande complexite technique du probleme. On donne la solution dans le cas general a l'aide de la theorie de spencer-goldschmidt
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Viviani, Emanuele. "Bihamiltonian structures on compact hermitian symmetric spaces." Doctoral thesis, 2022. http://hdl.handle.net/2158/1268162.

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In this thesis, we discuss a new approach to the problem of the diagonalization of the Nijenhuis tensor on compact hermitian symmetric spaces. Our attention is more focused on the hamiltonian forms rather than on the eigenvalues of the Nijenhuis tensor. This is motivated by the fact that the eigenvalues of N are only continuous functions and their derivatives have singularities. We describe these hamiltonian forms in terms of polynomials invariant with respect to a chain of subalgebra.
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Book chapters on the topic "Bihamiltonian"

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Duplij, Steven, Joshua Feinberg, Moshe Moshe, Soon-Tae Hong, Omer Faruk Dayi, Omer Faruk Dayi, Francois Gieres, et al. "Bihamiltonian Reduction and SKdVs." In Concise Encyclopedia of Supersymmetry, 58–60. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_63.

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Morales, J. J., and R. Ramirez. "Bihamiltonian Systems and Lax Representation." In Hamiltonian Mechanics, 253–59. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-0964-0_24.

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Olver, Peter J. "Canonical Forms for Bihamiltonian Systems." In Integrable Systems, 239–49. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0315-5_12.

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Casati, Paolo, Franco Magri, and Marco Pedroni. "Bihamiltonian Manifolds And Sato’s Equations." In Integrable Systems, 251–72. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0315-5_13.

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Casati, Paolo, Franco Magri, and Marco Pedroni. "The Bihamiltonian Approach to Integrable Systems." In Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, 101–10. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2050-0_10.

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Olver, P. J. "Canonical Forms for Compatible BiHamiltonian Systems." In Solitons and Chaos, 171–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84570-3_21.

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Kosmann-Schwarzbach, Y. "Generalized Symmetries, Recursion Operators and Bihamiltonian Systems." In Partially Intergrable Evolution Equations in Physics, 479–89. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-009-0591-7_18.

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Gelfand, Israel M., and Ilya Zakharevich. "On the Local Geometry of a Bihamiltonian Structure." In The Gelfand Mathematical Seminars, 1990–1992, 51–112. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0345-2_6.

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Liu, Si-Qi. "Lecture Notes on Bihamiltonian Structures and Their Central Invariants." In B-Model Gromov-Witten Theory, 573–625. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94220-9_7.

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Zubelli, Jorge. "The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems." In The Bispectral Problem, 139–55. Providence, Rhode Island: American Mathematical Society, 1998. http://dx.doi.org/10.1090/crmp/014/12.

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