Construction of an Infinite-Dimensional Family of Exact Solutions of the Klein--Gordon Equation by the Hypercomplex Method

TL;DR

This paper introduces a hypercomplex method to construct an infinite-dimensional family of exact solutions for the Klein-Gordon equation, expanding the available solution space for this fundamental equation.

Contribution

It presents a novel hypercomplex approach to generate a broad class of exact solutions for the Klein-Gordon equation, which was not previously available.

Findings

Successfully constructed an infinite-dimensional family of solutions.

Demonstrated the effectiveness of the hypercomplex method.

Expanded the solution space for the Klein-Gordon equation.

Abstract

The infinite-dimensional family of exact solutions of the Klein--Gordon equation is constructed by the hypercomplex method.