dorsal/arxiv
View SchemaWhat is the relativistic Volterra lattice?
| Authors | Yuri B. Suris, Orlando Ragnisco |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9802016 |
| URL | https://arxiv.org/abs/solv-int/9802016 |
| DOI | 10.1007/s002200050537 |
| Journal | Commun. Math. Phys., 1999, V. 200, p. 445--485. |
Abstract
We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problems, which can be, in turn, interpreted as new discrete time systems. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then ''relativistic'', the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the ''relativistic'' deformations were not known previously.
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"abstract": "We develop a systematic procedure of finding integrable \u0027\u0027relativistic\u0027\u0027\n(regular one-parameter) deformations for integrable lattice systems. Our\nprocedure is based on the integrable time discretizations and consists of three\nsteps. First, for a given system one finds a local discretization living in the\nsame hierarchy. Second, one considers this discretization as a particular\nCauchy problem for a certain 2-dimensional lattice equation, and then looks for\nanother meaningful Cauchy problems, which can be, in turn, interpreted as new\ndiscrete time systems. Third, one has to identify integrable hierarchies to\nwhich these new discrete time systems belong. These novel hierarchies are\ncalled then \u0027\u0027relativistic\u0027\u0027, the small time step $h$ playing the role of\ninverse speed of light. We apply this procedure to the Toda lattice (and\nrecover the well-known relativistic Toda lattice), as well as to the Volterra\nlattice and a certain Bogoyavlensky lattice, for which the \u0027\u0027relativistic\u0027\u0027\ndeformations were not known previously.",
"arxiv_id": "solv-int/9802016",
"authors": [
"Yuri B. Suris",
"Orlando Ragnisco"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1007/s002200050537",
"journal_ref": "Commun. Math. Phys., 1999, V. 200, p. 445--485.",
"title": "What is the relativistic Volterra lattice?",
"url": "https://arxiv.org/abs/solv-int/9802016"
},
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