dorsal/arxiv
View SchemaFunctional representation of the Ablowitz-Ladik hierarchy. II
| Authors | V. E. Vekslerchik |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9812020 |
| URL | https://arxiv.org/abs/solv-int/9812020 |
| DOI | 10.2991/jnmp.2002.9.2.3 |
| Journal | J. Nonlinear Math. Phys. 9, no. 2 (2002) 157-180 |
Abstract
In this paper I continue studies of the functional representation of the Ablowitz-Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition I rederive the functional equations for the tau-functions of the ALH and obtain some new equations which provide more straightforward description of the ALH and which were absent in the previous paper. These results are used to establish relations between the ALH and the discrete-time nonlinear Schrodinger equations, to deduce the superposition formulae (Fay's identities) for the tau-functions of the hierarchy and to obtain some new results related to the Lax representation of the ALH and its conservation laws. Using the previously found connections between the ALH and other integrable systems I derive functional equations which are equivalent to the AKNS, derivative nonlinear Schrodinger and Davey-Stewartson hierarchies.
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"abstract": "In this paper I continue studies of the functional representation of the\nAblowitz-Ladik hierarchy (ALH). Using formal series solutions of the\nzero-curvature condition I rederive the functional equations for the\ntau-functions of the ALH and obtain some new equations which provide more\nstraightforward description of the ALH and which were absent in the previous\npaper. These results are used to establish relations between the ALH and the\ndiscrete-time nonlinear Schrodinger equations, to deduce the superposition\nformulae (Fay\u0027s identities) for the tau-functions of the hierarchy and to\nobtain some new results related to the Lax representation of the ALH and its\nconservation laws. Using the previously found connections between the ALH and\nother integrable systems I derive functional equations which are equivalent to\nthe AKNS, derivative nonlinear Schrodinger and Davey-Stewartson hierarchies.",
"arxiv_id": "solv-int/9812020",
"authors": [
"V. E. Vekslerchik"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.2991/jnmp.2002.9.2.3",
"journal_ref": "J. Nonlinear Math. Phys. 9, no. 2 (2002) 157-180",
"title": "Functional representation of the Ablowitz-Ladik hierarchy. II",
"url": "https://arxiv.org/abs/solv-int/9812020"
},
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