dorsal/arxiv
View Schema'Universality' of the Ablowitz-Ladik hierarchy
| Authors | V. E. Vekslerchik |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9807005 |
| URL | https://arxiv.org/abs/solv-int/9807005 |
Abstract
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide range of solutions for, e.g., the 2D Toda lattice, nonlinear Schr\"odinger, Davey-Stewartson, Kadomtsev-Petviashvili (KP) and some other equations. Similar approach has been used to construct new integrable models: O(3,1) and multi-field sigma models. Such 'universality' of the ALH becomes more transparent in the framework of the Hirota's bilinear method. The ALH, which is usually considered as an infinite set of differential-difference equations, has been presented as a finite system of functional-difference equations, which can be viewed as a generalization of the famous bilinear identities for the KP tau-functions.
{
"annotation_id": "9fbeaaeb-e300-4106-af27-b0721097bb01",
"date_created": "2026-03-02T18:02:51.558000Z",
"date_modified": "2026-03-02T18:02:51.558000Z",
"file_hash": "5466eb18108397de9c10901426d1c6c88ec8cfccbd7ce8280c3c55d358c0e670",
"private": false,
"record": {
"abstract": "The aim of this paper is to summarize some recently obtained relations\nbetween the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It\nhas been shown that solutions of finite subsystems of the ALH can be used to\nderive a wide range of solutions for, e.g., the 2D Toda lattice, nonlinear\nSchr\\\"odinger, Davey-Stewartson, Kadomtsev-Petviashvili (KP) and some other\nequations. Similar approach has been used to construct new integrable models:\nO(3,1) and multi-field sigma models. Such \u0027universality\u0027 of the ALH becomes\nmore transparent in the framework of the Hirota\u0027s bilinear method. The ALH,\nwhich is usually considered as an infinite set of differential-difference\nequations, has been presented as a finite system of functional-difference\nequations, which can be viewed as a generalization of the famous bilinear\nidentities for the KP tau-functions.",
"arxiv_id": "solv-int/9807005",
"authors": [
"V. E. Vekslerchik"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "\u0027Universality\u0027 of the Ablowitz-Ladik hierarchy",
"url": "https://arxiv.org/abs/solv-int/9807005"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "dc561d99-c001-42f7-bf61-199d96892c2b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}