Journal ArticleDOI
Integrable mappings and soliton equations II
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TLDR
In this article, it was shown that simple solutions of discrete soliton equations satisfy 2D mappings and that these belong to a recently introduced 18-parameter family of integrable reversible mappings of the plane.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1989-01-01. It has received 408 citations till now. The article focuses on the topics: Integrable system & Soliton.read more
Citations
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Symplectic maps, variational principles, and transport
TL;DR: In this article, a Lagrangian variational formulation of twist maps is proposed to compute the flux escaping from regions bounded by partial barriers formed from minimizing orbits, which form a scaffold in the phase space and constrain the motion of remaining orbits.
Journal ArticleDOI
Time-reversal symmetry in dynamical systems: a survey
TL;DR: A survey of time-reversal symmetry in dynamical systems can be found in this paper, where the relation of time reversible dynamical sytems to equivariant and Hamiltonian systems is discussed.
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Wave transmission in nonlinear lattices
D. Hennig,G.P. Tsironis +1 more
TL;DR: In this paper, wave transmission properties in one dimensional nonlinear lattices are discussed and the results from the theory of dynamical systems are used to investigate various aspects of wave transmission and wave localization.
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Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems
TL;DR: In this article, the authors introduce reversible dynamical systems, which generalise classical mechanical systems possessing time-reversal symmetry and are found in ordinary differential equations, partial differential equations and diffeomorphisms (mappings) modelling many physical problems.
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On the extension of the Painlevé property to difference equations
TL;DR: In this paper, it is argued that the integrability of many difference equations is related to the structure of their solutions at infinity in the complex plane and that Nevanlinna theory provides many of the concepts necessary to detect integranability in a large class of equations.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book
Exactly solved models in statistical mechanics
TL;DR: In this article, exactly solved models of statistical mechanics are discussed. But they do not consider exactly solvable models in statistical mechanics, which is a special issue in the statistical mechanics of the classical two-dimensional faculty of science.
Mathematical methods of classical mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Journal ArticleDOI
A polynomial invariant for knots via von Neumann algebras
TL;DR: In this paper, it was shown that (6, n) and (c, ra) represent the same closed braid (up to link isotopy) if and only if they are equivalent for the equivalence relation generated by Markov moves of types 1 and 2 on the disjoint union of the braid groups.
Book
Solitons in mathematics and physics
TL;DR: The history of the Soliton derivation of the Korteweg-de Vries, nonlinear Schrodinger and other important and Canonical Equations of Mathematical Physics Soliton Equation families and Solution Methods The -Function, the Hirota Method, the Painleve Property and Backlund Transformations for the KORTewegde Vrie Family of Soliton Eq.