Abstract
This study continues an earlier investigation of applications of the method of noncommutative integration of linear partial differential equations [A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 1995; No. 5, 33 (1991)], which was a generalization of the analogous method for Hamiltonian systems. The method of noncommutative integration uses nonabelian algebra to characterize the symmetry of the equation, which makes it possible to construct exact solutions going beyond the framework of the method of separation of variables. The condition of noncommutative integrability is used to select the algebras of waveequation symmetry needed for the given method in Minkowski space R1,2. Nonequivalent noncommutative subalgebras of conformal algebra k1,2 are used to construct the basis of solutions of the three-dimensional wave equation.
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