Construction of an infinite-dimensional family of exact solutions of the Klein–Gordon equation by the hypercomplex method

The Klein–Gordon equation is one of the fundamental equations of mathematical physics. Therefore, it is important to have exact solutions to this equation. There are many methods for constructing exact solutions to the Klein–Gordon equation. Naturally, that different methods give different exact solutions. In this paper, by the hypercomplex method, we construct an infinite-dimensional new family of exact solutions of the polynomial–exponential type to the Klein–Gordon equation.