Noncommutative 5-dimensional subalgebras of a conformal algebra integrable in R1,3

The present study is concerned with the application and investigation of a new method of exact integration of systems of linear differential equations, the method of noncommutative integration. The method is based on the use of noncommutative subalgebras of symmetry for finding an exact solution. The investigation of 5-dimensional subalgebras of symmetry of the d'Alembert equation lead to the claim that there exists a class of subalgebras which generate exact solutions in explicit form but which it is not possible to obtain in explicit form by means of complete separation of the variables.Tomsk State University. Translated from Izvestiya Vysshikh Uchenbykh Zavedenii, Fizika, No. 6, pp. 115–119, June, 1995.