Alessandro Arsie, Paolo Lorenzoni, Antonio Moro
We propose an extension of Dubrovin's perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of first few corrections leads to conjecture that such normal forms are parametrized by one functional parameter named viscous central invariant. A constant valued central invariant gives the well known Burgers hierarchy. Remarkably, a linear viscous central invariant provides an apparently new integrable hierarchy. A detailed analytical and numerical study is devoted to a particular equation of this new hierarchy that can be viewed as a viscous analog of the Camassa-Holm equation. Asymptotic solutions via quasi-Miura transformations and transport equations as well as Dubrovin's Universality are also discussed.
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http://arxiv.org/abs/1301.0950
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