Integrable mappings and nonlinear integrable lattice equations

Papageorgiou, V.; Nijhoff, F.W.; Capel, H.W.

doi:10.1016/0375-9601(90)90876-p

Cited by 146 publications

(153 citation statements)

References 30 publications

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“…Such mappings can arise as periodic solutions of partial difference analogues of equations of KdV type, cf. [7,8]. Since these are the discrete analogues of the finite-gap potentials in the continuous theory, it is natural to expect that analogous methods can be applied to these discrete models as the ones used to deal with periodic problems in the continuous case.…”

Section: Introductionmentioning

confidence: 99%

Discrete Dubrovin equations and separation of variables for discrete systems

Nijhoff

2000

Chaos, Solitons & Fractals

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A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions in terms of Abelian functions of Kleinian type (i.e. the higher-genus analogues of the Weierstrass elliptic functions) is discussed as well as the connections with the method of separation of variables.

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Section: Introductionmentioning

confidence: 99%

Discrete Dubrovin equations and separation of variables for discrete systems

Nijhoff

2000

Chaos, Solitons & Fractals

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“…Under some additional conditions the transfer maps turn out to be integrable. Here we will consider one family of transfer maps derived from the so-called standard periodic staircase initial value problem that was originally presented as a periodic initialvalue problem for integrable partial difference equations in [13,18]. In this framework (see e.g.…”

Section: Transfer Maps As Periodic Sequences Of Collisions and Integrmentioning

confidence: 99%

Relativistic collisions as Yang–Baxter maps

Kouloukas

2017

Physics Letters A

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We prove that one-dimensional elastic relativistic collisions satisfy the set-theoretical Yang-Baxter equation. The corresponding collision maps are symplectic and admit a Lax representation. Furthermore, they can be considered as reductions of a higher dimensional integrable Yang-Baxter map on an invariant manifold. In this framework, we study the integrability of transfer maps that represent particular periodic sequences of collisions.

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“…Другой популярный выбор -так называемый лестничный набор {u n,n , u n,n+1 | n ∈ Z} [28], который мы в настоящей работе не используем.…”

Section: основные определенияunclassified