Integrable viscous conservation laws

@article{Arsie2013IntegrableVC,
  title={Integrable viscous conservation laws},
  author={Alessandro Arsie and Paolo Lorenzoni and Antonio Moro},
  journal={Nonlinearity},
  year={2013},
  volume={28},
  pages={1859 - 1895}
}
We propose an extension of the Dubrovin–Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few corrections leads to the conjecture that such normal forms are parameterized by one single functional parameter, named the viscous central invariant. A constant valued viscous central invariant corresponds to the well-known Burgers hierarchy. The case of a linear viscous central invariant provides a… 

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