Abstract.
Associated to the family of third-order quasilinear scalar evolution equations is the geometry of point transformations. This geometry provides a framework from which to study the structure of conservation laws of the equation, and to study the special nature of the geometry of those equations which do possess conservation laws. There is an easy and obvious normal form for equations which possess at least one conservation law. The geometric structure of the equation gives rise to a simple yet much less obvious normal form for equations which possess at least two conservation laws.
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Foltinek, K. Third-order scalar evolution equations with conservation laws . Sel. math., New ser. 8, 201–235 (2002). https://doi.org/10.1007/s00029-002-8105-3
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DOI: https://doi.org/10.1007/s00029-002-8105-3