Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
نویسندگان
چکیده
منابع مشابه
Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studied for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax functions is that the corresponding bi-Hamiltonian structures are degenerate, i.e. the metric which defines the Hamiltonian structure has va...
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Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but will, in general, be curved. The induced curvature is studied, a main result being that these natural submanifolds carry a induced pencil of compatible metrics....
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In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the...
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where P+ is a differential operator whose coefficients are differential polynomials in u, that is, polynomials in u and its x-derivatives u (s~. (The subscript + may be ignored at this point: we introduce it so as not to conflict with the notation in the main body of the paper.) Since L, is an operator of order zero, for (1.2) to make sense P, must be chosen so that the commutator on the right ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1999
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.533015