dorsal/arxiv
View SchemaNonlinear Physics: Integrability, Chaos and Beyond
| Authors | M. Lakshmanan |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9709008 |
| URL | https://arxiv.org/abs/solv-int/9709008 |
| DOI | 10.1142/S0218127497001187 |
Abstract
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramatically raising our perception of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based information technology, magnetoelectronics, controlling and synchronization of chaos and secure communications, to name a few. These developments have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and payoffs ahead in the next few decades by tracing the early historical events, summarizing the revolutionary era of 1950-70 when many important new ideas including solitons and chaos were realized and reviewing the current status. Important open problems both at the basic and applied levels are discussed.
{
"annotation_id": "a65bb88f-290e-4996-9d30-c71303aa8a34",
"date_created": "2026-03-02T18:02:50.886000Z",
"date_modified": "2026-03-02T18:02:50.886000Z",
"file_hash": "3efad6bb9eb27a9c40c92f9ef472fcae806b8cfc3e2c93a6b30c542657c2403c",
"private": false,
"record": {
"abstract": "Integrability and chaos are two of the main concepts associated with\nnonlinear physical systems which have revolutionized our understanding of them.\nHighly stable exponentially localized solitons are often associated with many\nof the important integrable nonlinear systems while motions which are\nsensitively dependent on initial conditions are associated with chaotic\nsystems. Besides dramatically raising our perception of many natural phenomena,\nthese concepts are opening up new vistas of applications and unfolding\ntechnologies: Optical soliton based information technology, magnetoelectronics,\ncontrolling and synchronization of chaos and secure communications, to name a\nfew. These developments have raised further new interesting questions and\npotentialities. We present a particular view of some of the challenging\nproblems and payoffs ahead in the next few decades by tracing the early\nhistorical events, summarizing the revolutionary era of 1950-70 when many\nimportant new ideas including solitons and chaos were realized and reviewing\nthe current status. Important open problems both at the basic and applied\nlevels are discussed.",
"arxiv_id": "solv-int/9709008",
"authors": [
"M. Lakshmanan"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1142/S0218127497001187",
"title": "Nonlinear Physics: Integrability, Chaos and Beyond",
"url": "https://arxiv.org/abs/solv-int/9709008"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5660efe9-a30a-4d3f-86ac-a2057d2f5841",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}