Geodesic
Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction
Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1260-1293

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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. 
@article{IM2_2015_79_6_a6,
     author = {D. V. Tunitsky},
     title = {Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction},
     journal = {Izvestiya. Mathematics },
     pages = {1260--1293},
     publisher = {mathdoc},
     volume = {79},
     number = {6},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a6/}
}
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D. V. Tunitsky. Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction. Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1260-1293. http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a6/