On Hyperbolic Equations with a Translation Operator in Lowest Derivatives

Abstract

In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained are classical if the real part of the symbol of a differential-difference operator in the equation is positive.

Keywords

• hyperbolic equation
• differential-difference equation
• translation operator
• classical solution