Abstract
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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