dorsal/arxiv
View SchemaPeriod preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations
| Authors | P. G. Grinevich, M. U. Schmidt |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9412005 |
| URL | https://arxiv.org/abs/solv-int/9412005 |
| DOI | 10.1016/0167-2789(95)00139-U |
| Journal | Physica D Nr. 87, pp. 73-98 (1995) |
Abstract
Flows on the moduli space of the algebraic Riemann surfaces, preserving the periods of the corresponding solutions of the soliton equations are studied. We show that these flows are gradient with respect to some indefinite symmetric flat metric arising in the Hamiltonian theory of the Whitham equations. The functions generating these flows are conserved quantities for all the equations simultaneously. We show that for 1+1 systems these flows can be imbedded in a larger system of ordinary nonlinear differential equations with a rational right-hand side. Finally these flows are used to give a complete description of the moduli space of algebraic Riemann surfaces corresponding to periodic solutions of the nonlinear Schr\"odinger equation.
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"abstract": "Flows on the moduli space of the algebraic Riemann surfaces, preserving the\nperiods of the corresponding solutions of the soliton equations are studied. We\nshow that these flows are gradient with respect to some indefinite symmetric\nflat metric arising in the Hamiltonian theory of the Whitham equations. The\nfunctions generating these flows are conserved quantities for all the equations\nsimultaneously. We show that for 1+1 systems these flows can be imbedded in a\nlarger system of ordinary nonlinear differential equations with a rational\nright-hand side. Finally these flows are used to give a complete description of\nthe moduli space of algebraic Riemann surfaces corresponding to periodic\nsolutions of the nonlinear Schr\\\"odinger equation.",
"arxiv_id": "solv-int/9412005",
"authors": [
"P. G. Grinevich",
"M. U. Schmidt"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"doi": "10.1016/0167-2789(95)00139-U",
"journal_ref": "Physica D Nr. 87, pp. 73-98 (1995)",
"title": "Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations",
"url": "https://arxiv.org/abs/solv-int/9412005"
},
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