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Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants

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Abstract

We formulate several conjectures concerning the structure and properties of thenxn integrable nondiagonalizable hamiltonian systems of hydrodynamic type. Forn=3 our results are, in fact, complete: a 3×3 nondiagonalizable hamiltonian system is integrable if and only if it is weakly nonlinear (linearly degenerate).

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Authors
  1. E. V. Ferapontov
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Institute for Mathematical Modelling, Academy of Sciences of Russia, 125047, Miusskaya, 4, Moscow, Russia. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 257–262, May, 1994.

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Ferapontov, E.V. Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants. Theor Math Phys 99, 567–570 (1994). https://doi.org/10.1007/BF01016140

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  • DOI: https://doi.org/10.1007/BF01016140

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