Geodesic
Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 257-262

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We formulate several conjectures concerning the structure and general properties of the $n\times n$ integrable nondiagonalizable hamiltonian systems of hydrodynamic type. For $n=3$ our results are in fact complete: a $3\times 3$ nondiagonalizable hamiltonian system is integrable if and only if it is weakly nonlinear (linearly degenerate). 
@article{TMF_1994_99_2_a11,
     author = {E. V. Ferapontov},
     title = {Several conjectures and results in the theory of integrable {Hamiltonian} systems of hydrodynamic type, which do not possess {Riemann} invariants},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {257--262},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a11/}
}
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E. V. Ferapontov. Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 257-262. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a11/