TY - JOUR
T1 - Hamiltonian partial differential equations and Frobenius manifolds
JF - Russian Mathematical Surveys. Volume 63, Issue 6, 2008, Pages 999-1010
Y1 - 2008
A1 - Boris Dubrovin
AB - In the first part of this paper the theory of Frobenius manifolds\\r\\nis applied to the problem of classification of Hamiltonian systems of partial\\r\\ndifferential equations depending on a small parameter. Also developed is\\r\\na deformation theory of integrable hierarchies including the subclass of\\r\\nintegrable hierarchies of topological type. Many well-known examples\\r\\nof integrable hierarchies, such as the Kortewegâ€“de Vries, non-linear\\r\\nSchrÂ¨odinger, Toda, Boussinesq equations, and so on, belong to this\\r\\nsubclass that also contains new integrable hierarchies. Some of these new\\r\\nintegrable hierarchies may be important for applications. Properties of the\\r\\nsolutions to these equations are studied in the second part. Consideration\\r\\nis given to the comparative study of the local properties of perturbed and\\r\\nunperturbed solutions near a point of gradient catastrophe. A Universality\\r\\nConjecture is formulated describing the various types of critical behaviour\\r\\nof solutions to perturbed Hamiltonian systems near the point of gradient\\r\\ncatastrophe of the unperturbed solution.
PB - SISSA
UR - http://hdl.handle.net/1963/6471
U1 - 6416
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -