Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations
نویسندگان
چکیده
منابع مشابه
Lax pairs for the equations describing compatible nonlocal Poisson brackets of hydrodynamic type, and integrable reductions of the Lamé equations
In the present work, the nonlinear equations for the general nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived and the integrability of these equations by the method of inverse scattering problem is proved. For these equations, the Lax pairs with a spectral parameter are presented. Moreover, we demonstrate the integrability of the equations for some espe...
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In the present paper, we solve the problem of reducing to the simplest and convenient for our purposes, “canonical” form for an arbitrary pair of compatible nonlocal Poisson brackets of hydrodynamic type generated by metrics of constant Riemannian curvature (compatible Mokhov–Ferapontov brackets [1]) in order to get an effective construction of the integrable hierarchies related to all these co...
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In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solved. The compatible pairs of nonlocal Poisson brackets of hydrodynamic type ha...
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15 صفحه اولNonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies and the equations of associativity
In this paper we solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics and establish that this nontrivial special class of Hamiltonian operators is closely connected with the associativity equations of twodimensional topological quantum field theories and the theory of Frobenius manifolds. It is shown that the Hamiltonian operators of this cla...
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ژورنال
عنوان ژورنال: Theoretical and Mathematical Physics
سال: 2004
ISSN: 0040-5779
DOI: 10.1023/b:tamp.0000015071.25148.90