The Toda lattice. II. Existence of integrals

Flaschka, H.

doi:10.1103/physrevb.9.1924

Cited by 691 publications

(419 citation statements)

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“…The result reads In the next section we shall also consider the nonrelativistic (nonperiodic) Toda systems. As is well known [23,7], one can take In this subsection we sketch our construction in general terms. While we proceed, we shall make certain assumptions that will be verified in the special contexts of Subsects.…”

Section: An Explicit Description Of a Special Flowmentioning

confidence: 99%

Relativistic Toda systems

Ruijsenaars¹

1990

Commun.Math. Phys.

244

306

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Section: An Explicit Description Of a Special Flowmentioning

confidence: 99%

Relativistic Toda systems

Ruijsenaars¹

1990

Commun.Math. Phys.

244

306

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“…we can write the total shift operator T n as 6) where the partial shift operators T n , T n 1 , defined by T n u n;n 1 = u n+1;n 1 and T n 1 u n;n 1 = u n;n 1 +1 , are given by…”

Section: Discrete Multiscale Expansionmentioning

confidence: 99%

Multiscale Expansion and Integrability Properties of the Lattice Potential KdV Equation

Heredero¹,

Levi²,

Petrera³

et al. 2008

JNMP

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We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schrödinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schrödinger equation.

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“…Although I had intended to collect my works in this opportunity, a letter from Ford informed me that Hénon (France) [10] and Flaschka (USA) [11] had found the conserved quantities (of same number of particles) for the nonlinear lattice (12), which drove me to study new things instead of collecting my previous works. Furthermore, Flaschka gave solutions with arbitrary number of solitons (N soliton solutions) for the case of an infinitely long one-dimensional lattice [12], based on the discrete lattice version of the inverse scattering method that had been found by Kruskal et al for the KdV equation [13].…”

Section: Sequelmentioning

confidence: 99%