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Friday, July 31, 2020 | History

1 edition of The Problem of Integrable Discretization: Hamiltonian Approach found in the catalog.

The Problem of Integrable Discretization: Hamiltonian Approach

by Yuri B. Suris

  • 337 Want to read
  • 33 Currently reading

Published by Birkhäuser Basel in Basel .
Written in English


Edition Notes

Statementby Yuri B. Suris
SeriesProgress in Mathematics -- 219, Progress in Mathematics -- 219.
The Physical Object
Format[electronic resource] /
Pagination1 online resource (XXI, 1070 pages).
Number of Pages1070
ID Numbers
Open LibraryOL27082787M
ISBN 103034880162
ISBN 109783034880169
OCLC/WorldCa840290325

  The problem of integrable discretization has been sporadically studied since the mids, i.e. the dawn of the modern theory of integrable systems. For more than 30 years, various techniques have been developed to obtain integrable discretizations of continuous systems. An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity is called an inverse problem because it starts with the effects and then calculates the.

Yu. B. Suris: On an integrable discretization of the modified Korteweg-de Vries equation Phys. Lett. A, , , p. ; Yu. B. Suris: A note on an integrable discretization of the nonlinear Schrödinger equation Inverse Problems, , 13, p. However, this development took a sharp turn when Poincaré showed that most Hamiltonian systems are not integrable and gave arguments indicating the nonintegrability of the three-body problem. In the same negative direction lies Brun's discovery that the three-body problem has no algebraic integral except for the well-known classical ones and Cited by:

American Mathematical Society Charles Street Providence, Rhode Island or AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Cited by: 8.   We discretize the “time” variable of the mKdV equation and get an integrable differenti In this paper, we present an integrable semi-discretization of the modified Korteweg-deVries (mKdV) equation. The Problem of Integrable Discretization: Hamiltonian Approach Author: Jianqing Sun, Xingbiao Hu, Yingnan Zhang.


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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 §