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Communications in Mathematical Physics

, Volume 267, Issue 1, pp 117–139 | Cite as

On Hamiltonian Perturbations of Hyperbolic Systems of Conservation Laws, II: Universality of Critical Behaviour

  • Boris DubrovinEmail author
Article

Abstract

Hamiltonian perturbations of the simplest hyperbolic equation u t + a(u) u x = 0 are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution. Moreover, this behaviour is described by a special solution to an integrable fourth order ODE.

Keywords

Soliton Conservation Laws Poisson Bracket Hyperbolic System Approximate Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.SISSATriesteItaly

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