Geodesic
Hamiltonian PDEs and Frobenius manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 6, pp. 999-1010 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 Korteweg–de Vries, non-linear Schrödinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution. 
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B. A. Dubrovin. Hamiltonian PDEs and Frobenius manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 6, pp. 999-1010. http://geodesic.mathdoc.fr/item/RM_2008_63_6_a1/

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[8] T. Claeys, M. Vanlessen, “Universality of a double scaling limit near singular edge points in random matrix models”, Comm. Math. Phys., 273:2 (2007), 499–532 | DOI | MR | Zbl

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[10] T. Claeys, T. Grava, Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann–Hilbert approach, , 2008 arxiv: math/0801.2326

[11] B. Dubrovin, T. Grava, C. Klein, “On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the tritronquée solution to the Painlevé-I equation”, J. Nonlinear Sci. (to appear); , 2007 arxiv: math/0704.0501