Multidimensional Hyperbolic Equations with Nonlocal Potentials: Families of Global Solutions

Abstract

In spaces of arbitrary dimensions, hyperbolic differential–difference equations with potentials undergoing translations along arbitrary spatial directions are investigated. The fundamental novelty of this study is that, unlike previous investigations, no restrictions are imposed on the symbol of the differential–difference operator contained in the equation. For the investigated equation, we succeed to explicitly construct a multiparametric family of classical global solutions.

Keywords

• differential–difference operators
• multidimensional hyperbolic equations
• nonlocal potentials
• classical solutions