Abstract

A one-parameter family of smooth solutions of a two-dimensional differential-difference hyperbolic equation with \(n\) translations with respect to the spatial variable is constructed. The theorem is proved that the obtained solutions are classical if the real part of the symbol of the difference operator of the equation is positive. The class of equations such that the specified condition is satisfied for them and only for them is selected.

中文翻译：

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具有多个非局部项的双曲型微分方程的经典解

摘要

构造一维相对于空间变量具有（n \）个平移的二维微分双曲方程的单参数光滑解。该定理证明，如果方程的差分算子符号的实部为正，则所获得的解是经典的。满足特定条件且仅针对特定条件的方程式类别。