The Problem of Integrable Discretization: Hamiltonian Approach

The Problem of Integrable Discretization: Hamiltonian Approach by Yuri B. Suris Download PDF EPUB FB2

Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of.

Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of Cited by: Download Citation | The Problem of Integrable Discretization: Hamiltonian Approach | this paper.

Hence, the nature of this discretization as a member of the Toda hierarchy was not understood properly. I General Theory.- 1 Hamiltonian Mechanics.- The problem of integrable discretization.- Poisson brackets and Hamiltonian flows.- Symplectic manifolds.- Poisson submanifolds and symplectic leaves.- Dirac bracket.- Poisson reduction.- Complete integrability.- Bi-Hamiltonian systems.- Lagrangian mechanics on?N.- Lagrangian.

Get this from a library. The Problem of Integrable Discretization: Hamiltonian Approach. [Yuri B Suris] -- The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system.

Get this from a library. The problem of integrable discretization: Hamiltonian approach. [Yuri B Suris] -- "The book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography (about items) and.

Let us start with a precise formulation of the problem of integrable discretization. The notions used in this formulation are the fundamental notions of Hamiltonian mechanics. The main definitions and results thereof are collected in the subsequent sections of this chapter in.

The problem of integrable discretization. Hamiltonian approach (Birkhäuser, ) Consider a completely integrable flow x˙ = f() = {H, } (1) with a Hamilton function H on a Poisson manifold P with a Poisson bracket {,}.

Thus, the flow (1) possesses many functionally independent integrals Ik(x) in involution. An integrable semi-discretization of complex and multi-component coupled dispersionless systems via Lax pairs is presented.

A Lax pair is proposed for the complex sdCD system. The problem of integrable discretization: Hamiltonian approach A skeleton of the book By Y.B. Suris and Technische Univ. Berlin (Germany).

Sonderforschungsbereich -Differentialgeometrie und. The problem of integrable discretization. Hamiltonian approach (Birkhäuser, ) Consider a completely integrable flow x_ = f() = fH; g (1) with a Hamilton function H on a Poisson manifold Pwith a Poisson bracket f;g.

Thus, the flow (1) possesses many functionally independent integrals Ik(x) in involution. The problem of integrable discretization: Hamiltonian approach by Yuri B.

Suris - Progress in Mathematics, Volume Birkhäuser. 2 The problem of integrable discretization Let us formulate the problem of integrable discretization more precisely. Let X be a Poisson manifold with a Poisson bracket {,}.

Let Hbe a completely integrable Hamilton function on X, i.e. the system x˙ = {H,x} () possesses many enough functionally independent integrals Ik(x) in involution. Another famous integrable discretization of the KdV equation is the Volterra lattice [29, 22] dq s dt = q s(q s+1 q s 1): By the Miura transformation q s= p sp s 1, it is related to the equation dp s dt = p2 (3) s(p +1 p 1); which is the modi ed Volterra lattice, an integrable discretization of the modi ed KdV by: Books by Yuri B.

SURIS. Yu.B. Suris. The Problem of Integrable Discretization: Hamiltonian Approach. Flowing. Flowing Hair Dollar Bb B-5 3 Leaves Icg F12 Problem Free. $2, Nonlinear Evolution Equations A Hamiltonian Approach to the K dV and Other Equations Peter D.

Lax 1. Introduction. Recent investigations, originating in the fundamental work of Kruskal, Zabusky and Gardner reveal that a large num ber of equations governing nonlinear wave motion can be Cited by: 5. We consider the Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point with parameters in a complex domain.

We suppose that these equations admit a first integral functionally independent of the three already known integrals which does not depend on all the variables.

We prove that this may happen only in the already known three integrable cases or in the Author: Sasho Popov, Jean-Marie Strelcyn. The aim of the paper is to unify the efforts in the study of integrable billiards within quadrics in flat and curved spaces and to explore further the interplay of symplectic and contact integrability.

As a starting point in this direction, we consider virtual billiard dynamics within quadrics in pseudo-Euclidean : Božidar Jovanović, Vladimir Jovanović.

The problem of integrable discretization: Hamiltonian approach. Progress in Mathematics, Birkhauser Verlag, Basel, xxii+ pp. ISBN: Gesztesy, Fritz; Holden, Helge Soliton equations and their algebro-geometric solutions.

Vol. (1+1)-dimensional continuous models. Cambridge Studies in Advanced Mathematics. The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations.

For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one.Fu, Wei and Nijhoff, Frank W.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol.Issue.p. Cited by:   § Affine Hamiltonian Operators And Two-Cocycles On Lie Algebras, Etc.

; Chapter Hamiltonian Formalism For Discrete Integrable Systems Of KP And MKP Types § The KP-Type Systems § The MKP-Type Systems § The Miura Map From KP To MKP Is Hamiltonian §