Relevant bibliographies by topics / Bihamiltonian

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Bihamiltonian'

Author: Grafiati
Published: 10 March 2023
Last updated: 31 July 2025

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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 (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 la
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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 (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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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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Dinar, Yassir. "Low-dimensional bihamiltonian structures of topological type." Journal of Mathematical Physics 64, no. 3 (2023): 033502. http://dx.doi.org/10.1063/5.0130899.

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We construct local bihamiltonian structures from classical W-algebras associated with non-regular nilpotent elements of regular semisimple type in Lie algebras of types A2 and A3. They form exact Poisson pencils and admit a dispersionless limit, and their leading terms define logarithmic or trivial Dubrovin–Frobenius manifolds. We calculate the corresponding central invariants, which are expected to be constants. In particular, we get Dubrovin–Frobenius manifolds associated with the focused Schrödinger equation and Hurwitz space M0;1,0 and the corresponding bihamiltonian structures of topologi
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Casati, Paolo, Gregorio Falqui, Franco Magri та Marco Pedroni. "Bihamiltonian reductions and ωn-algebras". Journal of Geometry and Physics 26, № 3-4 (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 (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 (2016): 805–19. http://dx.doi.org/10.1007/s00220-015-2540-4.

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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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Casati, Paolo, and Giovanni Ortenzi. "Bihamiltonian Equations on Polynomial Virasoro Algebras." Journal of Nonlinear Mathematical Physics 13, no. 3 (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 (2001): 149–57. http://dx.doi.org/10.1016/s0034-4877(01)80074-4.

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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
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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 t
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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 struc
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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, et al. "Bihamiltonian Reduction and SKdVs." In Concise Encyclopedia of Supersymmetry. 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. 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. 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. 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. 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. 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. 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. 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. 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. American Mathematical Society, 1998. http://dx.doi.org/10.1090/crmp/014/12.

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