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Non-homogeneous systems of hydrodynamic type, related to quadratic Hamiltonians with electromagnetic term

✍ Scribed by E.V. Ferapontov; A.P. Fordy

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 633 KB
Volume: 108
Category: Article
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(97)00040-7

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✦ Synopsis

We consider a class of non-homogeneous systems of hydrodynamic type:

which can be related to quadratic Hamiltonians with electromagnetic terms. Whilst it is unlikely that our systems are generally integrable, they do possess intriguing properties, such as (always) having a higher conservation law and (sometimes) a 2nparameter family of exact solutions. In fact our systems coincide with those possessing a conservation law with the density E being a quadratic expression in the first derivatives:

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