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About 7,794 papers for “Integrable system”
Li Zhu, Yujuan Zhang · 2009
A hierarchy of integrable discrete equations is derived based on discrete isospectral problem. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Then, integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.
Cited by 2
N Supersymmetric, Yang-mills Theory, Kanehisa Takasaki · 1996
We study the exact solution of N = 2 supersymmetric SU(N) Yang-Mills theory in the framework of the Whitham-Toda hierarchy. We show that it is in fact obtainable by modulating the solution of the (generalized) Toda lattice associated with moduli of curves. The relation between the holomorphic pre-potential of the low energy effective action and the τ-function of the (generalized) Toda lattice is also clarified. Recently Seiberg and Witten 1 obtained exact expressions for the metric on moduli space and the dyon spectrum of N = 2 supersymmetric SU(2) Yang-Mills theory by using a version of the Montonen-Olive duality 2 and holomorphy 3 of 4d supersymmetric theories. Their approach has been generalized to the case of other Lie group 4 5. Especially surprising in these results is unexpected emergence of elliptic (or hyperelliptic) curves and their periods. Although these objects appear in the course of determining the holomorphic pre-potential F of the exact low energy effective actions, physical siginificance of the curves themselves is unclear yet. It will be important to clarify their physical role. An interesting step in this direction has been taken 6 from the view of integrable systems, in which the correspondence between the Seiberg-Witten solution 1 and a Gurevich-Pitaevsky solution 7 to the elliptic Whitham equations 8 is pointed out. The exact solution (Seiberg-Witten type) of N=2 supersymmetric SU(N) Yang-Mills theory is described by the following data 1 4: a Talk presented at the Workshop “Frontiers in Quantum Field Theory ” in honor of the
Cited by 0
Boris A. Kupershmidt · Physics Letters A · 2007
Cited by 97Open access
Fajun Yu, Hongqing Zhang · Physics Letters A · 2006
Cited by 23
Xiaohong Chen, Tiecheng Xia, Liancheng Zhu · Chinese Physics · 2007
This paper establishes a new isospectral problem. By making use of the Tu scheme, a new integrable system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.
Cited by 4
García, Marcos A. G., Turbiner, Alexander V · arXiv (Cornell University) · 2010
The quantum $H_4$ integrable system is a 4D system with rational potential related to the non-crystallographic root system $H_4$ with 600-cell symmetry. It is shown that the gauge-rotated $H_4$ Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group $H_4$, is in algebraic form: it has polynomial coefficients in front of derivatives. Any eigenfunctions is a polynomial multiplied by ground-state function (factorization property). Spectra corresponds to one of the anisotropic harmonic oscillator. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the characteristic vector $\vec \al\ =\ (1,5,8,12)$.
Cited by 0Open access
A. D. Bruno · Doklady Mathematics · 2014
Cited by 2
Weihua Mu, Cewen Cao, Xianguo Geng · Acta Mathematica Scientia · 1993
Cited by 0
Mustafa Mullahasanoğlu · Journal of Physics Conference Series · 2023
Abstract In this study, we work on a novel Hamiltonian system which is Liouville integrable. In the integrable Hamiltonian model, conserved currents can be represented as Binomial polynomials in which each order corresponds to the integral of motion of the system. From a mathematical point of view, the equations of motion can be written as integrable second-order nonlinear partial differential equations in 1 + 1 dimensions.
Cited by 0Open access
F. Calogero, Jean–Pierre Françoise · Journal of Mathematical Physics · 1996
The dynamical system characterized by the Hamiltonian H(q,p)=∑j,k=1n pjpkf(q dj−qk) with f(x)=λ+μ cos(νx)+μ′ sin(ν‖x‖) is completely integrable. Here n is an arbitrary positive integer and λ,μ,μ′,ν are 4 arbitrary constants (λ and μ real, μ′ and ν both real or both imaginary).
Cited by 58
Philip C. Argyres · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2023
In this work we establish that the Inozemtsev system is the Seiberg-Witten integrable system encoding the Coulomb branch physics of 4d <span class="mathjax-tex">\( \mathcal{N} \)</span> = 2 USp(2<em>N</em>) gauge theory with four fundamental and (for <em>N ≥</em> 2) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-forms of the Inozemtsev system in the <em>N</em> = 1 and <em>N</em> = 2 cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev system to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser systems with Seiberg-Witten integrable systems, which will be explored in future work.
Cited by 4Open access
Qingyou Yan, Yufeng Zhang, Xiaopeng Wei · Chaos Solitons & Fractals · 2003
Cited by 4
Koji Imai, Kimiaki Konno, Hiroshi Kakuhata · Journal of the Physical Society of Japan · 1999
By assuming the symmetry group and using the inverse method, we find an integrable system which is constructed from superposition of two hierarchies of integrable equations. We discuss S U (2) and S L (2, R ) cases in detail. Furthermore, we present a procedure to construct integrable equations by taking a coefficient in the hierarchies as function of x and t .
Cited by 6
Boris A. Kupershmidt · Physics Letters A · 1985
Cited by 10
Martin A. Guest · 2008
Abstract We have seen that the quantum cohomology of a manifold can be described as a flat connection or D-module. We have hinted that this puts it on the same footing as a solution of an integrable system. In this chapter we shall describe the WDVV (Witten–Dijkgraaf–Verlinde–Verlinde) equations, which provide suitable partial differential equations.
Cited by 1
Liuwang Zeng, Zhang Jun, Jing Li · 2024
This book addresses complex issues such as the existence of homoclinic orbits and the study of chaotic behavior arising from these orbits in various perturbed nonlinear equations, including the Schrödinger equation, the Sine-Gordon equation, and the Korteweg-de Vries (KdV) equation. It provides a detailed and rigorous examination of these topics, supported by rich documentation and illustrative examples. The content reflects fundamental concepts and significant advancements in nearly integrable dynamical systems. Designed to facilitate the rapid entry of senior university students, graduate students, postdoctoral fellows, and early-career academics into the field, this book also serves as a valuable reference for researchers and educators in traditional natural sciences and engineering, aiding in the expansion of their knowledge base.
Cited by 0
Hajjar, Ara · Library and Archives Canada (Government of Canada) · 1998
The growing need for integrable test solutions has prompted the creation of various test bus standards. A mixed-signal test core is an ideal complement to these standards. This work presents the design and implementation of an integrable test system. The design consists of two major components: a stimulus generator, and a waveform extractor.
Cited by 0
Qi Li · 2009
The integrable equations with self-consistent sources is one kind of important nonlinear evolution equations. The studies of its integrable and solutions have important mathematics senses. It is used to describe interactions between different solitary waves and has important physical applications. We introduce the concept of Lax integrable and give the hierarchy of the non-isospectral KdV equation with self-consistent sources(KdVESCS )and the hierarchy of the non-isospectral AKNS equation with self-consistent sources(AKNS ESCS ) as examples.
Cited by 0
G. Sardanashvily · 2002
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Physics Letters A, Spatiotemporal Chaos, David Cai et al. · 1999
We address (i) the onset of spatiotemporal chaos (STC) induced by the hyperbolic structure in a weakly perturbed nonlinear Schrijdinger equation, and (ii) its effective stochastic dynamics (ESD). We obtain the following new results: ( 1) a very small number (two for our system) of linearly unstable modes is sufficient to trigger the onset of STC as characterized by an exponential decay in space of the mutual information; (2) the construction of the ESD needs only remporal chaos, in contrast to the requirement of full STC as usually believed. @ 1999 Elsevier Science B.V.
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