Abstract:
This paper is devoted to systems of $n$ inhomogeneous equations
of hydrodynamic type with two independent variables. Using a geometric
formalism for such systems which goes back to Riemann, one can
associate with every system of hydrodynamic type a vector field and
a field of linear operators acting on an appropriate tangent bundle.
In terms of these fields, we obtain a number of tests for inhomogeneous
systems of hydrodynamic type to be decoupled into subsystems with
block-triangular interaction. These tests supplement Bogoyavlenskii's
well-known results on decoupling of homogeneous systems of hydrodynamic
type into non-interacting subsystems.
Keywords:systems of hydrodynamic type, non-interacting subsystems, subsystems with block-triangular interaction, Nijenhuis tensor.
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