# A Deformation of the Method of Characteristics and the Cauchy Problem for Hamiltonian PDEs in the Small Dispersion Limit

@article{Masoero2012ADO, title={A Deformation of the Method of Characteristics and the Cauchy Problem for Hamiltonian PDEs in the Small Dispersion Limit}, author={Davide Masoero and Andrea Raimondo}, journal={International Mathematics Research Notices}, year={2012}, volume={2015}, pages={1200-1238} }

We introduce a deformation of the method of characteristics valid for Hamiltonian perturbations of a scalar conservation law in the small dispersion limit. Our method of analysis is based on the 'variational string equation', a functional-differential relation originally introduced by Dubrovin in a particular case, of which we lay the mathematical foundation.
Starting from first principles, we construct the string equation explicitly up to the fourth order in perturbation theory, and we show…

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