Geodesic
Breaking solitons. VI. Extension of systems of hydrodynamic type
Izvestiya. Mathematics, Tome 39 (1992) no. 2, pp. 959-973 
O. I. Bogoyavlenskii. Breaking solitons. VI. Extension of systems of hydrodynamic type. Izvestiya. Mathematics, Tome 39 (1992) no. 2, pp. 959-973. http://geodesic.mathdoc.fr/item/IM2_1992_39_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Systems of differential equations, admitting the Lax representation and extending the systems of hydrodynamic type, connected with the Volterra model and Toda lattice, are presented. A construction of differential operator equations with derivatives of arbitrary order with respect to the variables $t$ and $y$ and possessing a reduction preserving the eigenvalues of the corresponding operator $L$ is suggested. Dynamical systems having a Lax representation and generalizing the Toda lattice are constructed. A construction of integrable Euler equations admitting a Lax representation with $n$ independent spectral parameters and connected with $n$ Riemann surfaces is found.

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