1989
DOI: 10.1070/rm1989v044n06abeh002300
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Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory

Abstract: CONTENTSIntroduction 35 Chapter I. Hamiltonian theory of systems of hydrodynamic type 45 § 1. General properties of Poisson brackets 45 §2. Hamiltonian formalism of systems of hydrodynamic type and 55 Riemannian geometry §3. Generalizations: differential-geometric Poisson brackets of higher orders, 66 differential-geometric Poisson brackets on a lattice, and the Yang-Baxter equation §4. Riemann invariants and the Hamiltonian formalism of diagonal systems 71 of hydrodynamic type. Novikov's conjecture. Tsarev's … Show more

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Cited by 407 publications
(631 citation statements)
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References 64 publications
(72 reference statements)
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“…Another implication of the developed theory is the thermodynamic limit for the Krichever algebro-geometrical procedure of integration of the Whitham equations [18], [11]. This result will be published in a separate paper [19].…”
Section: Averaged Conservation Lawsmentioning
confidence: 99%
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“…Another implication of the developed theory is the thermodynamic limit for the Krichever algebro-geometrical procedure of integration of the Whitham equations [18], [11]. This result will be published in a separate paper [19].…”
Section: Averaged Conservation Lawsmentioning
confidence: 99%
“…Then an extensive cancellation becomes possible in (34) so that the hyperelliptic integrals in (11), (12) turn into elementary ones. As a result, we have the following asymptotics (see [7] for details):…”
Section: The Thermodynamic Limit For the Rotation Numbers: Basic Intementioning
confidence: 99%
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“…For the modified KP ͑mKP͒ hierarchy the operator L is of the form Lϭ‫ץ‬ϩu 0 ϩu 1 ‫ץ‬ Ϫ1 ϩu 2 ‫ץ‬ Ϫ2 ϩ¯while for the two-dimensional Toda lattice ͑2DTL͒ hierarchy one needs two operators L 1 and L 2 . 10 The dispersionless KP ͑dKP͒ hierarchy is a formal limit →0 of the KP hierarchy for which [1][2][3][4][5][6][7][8][9][10] .5͒ or ͑2.6͒ represent the dKP hierarchy. Similarly, the dmKP hierarchy is given by equations of the form ͑2.5͒-͑2.7͒ with Lϭpϩ ͚ nϭ1 ϱ u n (T)p Ϫn .…”
Section: Dispersionless Hierarchies and Universal Whitham Hierarchymentioning
confidence: 99%