Hamiltonian equations in R-3

Download

index.pdf

Date

2003-12-01

Author

Ay, Ahmet
GÜRSES, METİN
Zheltukhın, Kostyantyn

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

258
views

0
downloads

The Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in R-3 is proposed. The form of the solution is shown to be valid also in the neighborhood of some irregular points. Compatible Poisson structures and corresponding bi-Hamiltonian systems are also discussed. Hamiltonian structures, the classification of irregular points and the corresponding reduced first order differential equations of several examples are given. (C) 2003 American Institute of Physics.

Subject Keywords

Mathematical Physics, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/42000

Journal

JOURNAL OF MATHEMATICAL PHYSICS

DOI

https://doi.org/10.1063/1.1619204

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Dynamical systems and Poisson structures Guerses, Metin; Guseinov, Gusein Sh; Zheltukhın, Kostyantyn (AIP Publishing, 2009-11-01) We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that al...
Hydrodynamic type integrable equations on a segment and a half-line Guerses, Metin; Habibullin, Ismagil; Zheltukhın, Kostyantyn (AIP Publishing, 2008-10-01) The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable reductions in multifield systems is observed. The problem of consistency of boundary conditions with the Hamiltonian formulation is discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a segment and a semiline are presented. (C) 2008 American Institut...
Quantum duality, unbounded operators, and inductive limits Dosi, Anar (AIP Publishing, 2010-06-01) In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
Integrability of Kersten-Krasil'shchik coupled KdV-mKdV equations: singularity analysis and Lax pair Karasu, Emine Ayşe; Yurdusen, I (AIP Publishing, 2003-04-01) The integrability of a coupled KdV-mKdV system is tested by means of singularity analysis. The true Lax pair associated with this system is obtained by the use of prolongation technique. (C) 2003 American Institute of Physics.
String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication Kondo, Satoshi; Watari, Taizan (Springer Science and Business Media LLC, 2019-04-01) It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Bo...

Citation Formats

A. Ay, M. GÜRSES, and K. Zheltukhın, “Hamiltonian equations in R-3,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 5688–5705, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42000.