Abstract:
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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