Abstract
This paper aims at investigating necessary (and sufficient) conditions for quasilinear systems of first order PDEs to be Hamiltonian, with non-homogeneous operators of order \(1+0\), also with degenerate leading coefficient. As a byproduct, Tsarev’s compatibility conditions are extended to degenerate operators. Some examples are finally discussed.
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Acknowledgements
The author thanks R. Vitolo, M. Menale and M. Dell’Atti for stimulating discussions. The author also acknowledges the financial support of GNFM of the Istituto Nazionale di Alta Matematica, of PRIN 2017 “Multiscale phenomena in Continuum Mechanics: singular limits, off-equilibrium and transitions”, project number 2017YBKNCE and of the research project Mathematical Methods in Non-Linear Physics (MMNLP) by the Commissione Scientifica Nazionale – Gruppo 4 – Fisica Teorica of the Istituto Nazionale di Fisica Nucleare (INFN).
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Vergallo, P. Non-homogeneous Hamiltonian structures for quasilinear systems. Boll Unione Mat Ital 17, 513–526 (2024). https://doi.org/10.1007/s40574-023-00369-5
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DOI: https://doi.org/10.1007/s40574-023-00369-5