dorsal/arxiv
View SchemaClassification of evolutionary equations on the lattice. I. The general theory
| Authors | D. Levi, R. Yamilov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9511006 |
| URL | https://arxiv.org/abs/solv-int/9511006 |
Abstract
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n, u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the well-known Volterra and Toda equations can be written in this form). If before, in the framework of the symmetry approach, only equations similar to $$ u_{n,t} = f(u_{n-1}, u_n, u_{n+1}), $$ i.e. defined by a function $f$, were considered, now we have an infinite set $f_n$ of a priori quite different functions.
{
"annotation_id": "bd786cb1-78f4-436e-89a9-ba96b951372e",
"date_created": "2026-03-02T18:02:51.153000Z",
"date_modified": "2026-03-02T18:02:51.153000Z",
"file_hash": "75ef02488246f94edeecfebf1a4cf3b73c28752fbd187c465dd2037232f624d6",
"private": false,
"record": {
"abstract": "A modification of the symmetry approach for the classification of integrable\ndifferential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n,\nu_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the\nwell-known Volterra and Toda equations can be written in this form). If before,\nin the framework of the symmetry approach, only equations similar to $$ u_{n,t}\n= f(u_{n-1}, u_n, u_{n+1}), $$ i.e. defined by a function $f$, were considered,\nnow we have an infinite set $f_n$ of a priori quite different functions.",
"arxiv_id": "solv-int/9511006",
"authors": [
"D. Levi",
"R. Yamilov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Classification of evolutionary equations on the lattice. I. The general theory",
"url": "https://arxiv.org/abs/solv-int/9511006"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "542e98b0-a088-4275-9d48-a0ec4275775f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}