A deformation of the method of characteristics and the Cauchy problem for Hamiltonian PDEs in the small dispersion limit
2012-12-07 14:30 2012-12-07 15:30 2012-12-07 14:30 .. 15:30
Andrea Raimondo (SISSA, International School for Advanced Studies, Trieste)
In this talk, I will consider a deformation of the method of characteristics valid for Hamiltonian perturbations of a scalar conservation law in the small dispersion limit. The method of analysis is based on the ‘variational string equation’, a functional-differential relation originally introduced by Dubrovin in a particular case, of which I will describe the mathematical foundation. Considering in detail the example of the KdV equation, I will prove the validity of the string equation in the small dispersion limit, and explicitly compute the first two perturbative corrections of the KdV solution. If time permits, I will extend the construction to more general (non integrable) perturbations. The talk is based on a recent joint work with Davide Masoero.