Geodesic
Breaking solitons. VI.~Extension of systems of hydrodynamic type
Izvestiya. Mathematics , Tome 39 (1992) no. 2, pp. 959-973

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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. 
@article{IM2_1992_39_2_a1,
     author = {O. I. Bogoyavlenskii},
     title = {Breaking solitons. {VI.~Extension} of systems of hydrodynamic type},
     journal = {Izvestiya. Mathematics },
     pages = {959--973},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_39_2_a1/}
}
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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/