Geodesic
Reducing quasilinear systems to block triangular form
Sbornik. Mathematics, Tome 204 (2013) no. 3, pp. 438-462

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The paper is concerned with systems of $n$ quasilinear partial differential equations of the first order with 2 independent variables. Using a geometric formalism for such equations, which goes back to Riemann, it is possible to assign a field of linear operators on an appropriate vector bundle to this type of quasilinear system. Several tests for a quasilinear system to be reducible to triangular or block triangular form are obtained in terms of this field; they supplement well known results on diagonalization and block diagonalization due to Haantjes and Bogoyavlenskij. Bibliography: 10 titles.
Keywords: block triangular quasilinear systems, block diagonal quasilinear systems, fields of linear operators, Nijenhuis tensors, Haantjes tensors. 
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     author = {D. V. Tunitsky},
     title = {Reducing quasilinear systems to block triangular form},
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D. V. Tunitsky. Reducing quasilinear systems to block triangular form. Sbornik. Mathematics, Tome 204 (2013) no. 3, pp. 438-462. http://geodesic.mathdoc.fr/item/SM_2013_204_3_a5/