# On universality of critical behaviour in Hamiltonian PDEs

@article{Dubrovin2008OnUO, title={On universality of critical behaviour in Hamiltonian PDEs}, author={Boris Dubrovin}, journal={arXiv: Analysis of PDEs}, year={2008} }

Our main goal is the comparative study of singularities of solutions to the systems of first order quasilinear PDEs and their perturbations containing higher derivatives. The study is focused on the subclass of Hamiltonian PDEs with one spatial dimension. For the systems of order one or two we describe the local structure of singularities of a generic solution to the unperturbed system near the point of "gradient catastrophe" in terms of standard objects of the classical singularity theory; we…

## 57 Citations

### Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions

- Mathematics
- 2009

We begin with presentation of classification results in the theory of Hamiltonian PDEs with one spatial dimension depending on a small parameter. Special attention is paid to the deformation theory…

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It is argued that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P$$_I$$I) equation or its fourth-order analogue P$$-I^2$$I2.

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### Hamiltonian PDEs and Frobenius manifolds

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