Abstract
In this paper, we continue an investigation of applications of the method of noncommutative integration of linear differential equations in partial derivatives (A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fizika., No. 4, 116 (1991); ibid., No. 5, 100 (1991)). We demonstrate the application of quadratic algebras (allowing for second-order operators) to the problem of constructing an exact basis for solutions of the wave equation in unseparated variables. For a nontrivial example, we have integrated the three-dimensional wave equation using a nonabelian quadratic algebra.
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