seminar at SIssa

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR ACTIVITIES
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SEMINAR ON:
"Deformations of Whitham systems and Lagrangian formalism"

Dott. Andrey MALTSEV

Abstract: We consider the deformations of Whitham systems including the
"dispersion terms" and having the form of Dubrovin-Zhang deformations of
Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem
of deformations of Frobenius manifolds corresponding to the Whitham systems
of integrable hierarchies. Under some non-degeneracy requirements we suggest
a general scheme of the deformation of the hyperbolic Whitham systems using
the initial non-linear system. The general form of the deformed Whitham
system coincides with the form of the "low-dispersion" asymptotic expansions
used by B.A. Dubrovin and Y. Zhang in the theory of deformations of
Frobenius manifolds. We consider also a Lagrangian formalism of the deformed
systems as a convenient tool of the construction of deformations. As an
example the case of modulated one-phase solutions of the non-linear
"V-Gordon" equation is considered.




Wed. 18 October 2006 @ 14.30
SISSA - Main Building - lower ground floor - room D