Geodesic
Breaking solitons. V.~Systems of hydrodynamic type
Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 439-454

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A method for constructing the systems of hydrodynamic type having a number of Riemann invariants is indicated. The method is based on a new differential equation in a space of linear operators. The systems of hydrodynamic type naturally connected with the Volterra model and the Toda lattice are constructed. Their continuous limits are found, the equation (see [1] and [2]) of interaction between Riemann breaking waves and transversal long waves is among them. The equations for self-similar solutions of homogeneous systems of hydrodynamic type are derived. 
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     author = {O. I. Bogoyavlenskii},
     title = {Breaking solitons. {V.~Systems} of hydrodynamic type},
     journal = {Izvestiya. Mathematics },
     pages = {439--454},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a0/}
}
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O. I. Bogoyavlenskii. Breaking solitons. V.~Systems of hydrodynamic type. Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 439-454. http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a0/