Abstract For a two-dimensional hyperbolic equation with a differential-difference operator acting with respect to the spatial variable, we construct a one-parameter family of global solutions. We prove that these solutions are classical for all values of the real parameter provided that the real part of the symbol of the difference operator occurring in the equation is positive. We present a class of equations for which this condition is satisfied.

中文翻译：

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一些二维双曲微分方程的全局经典解

摘要 对于一个二维双曲方程，其微分差分算子作用于空间变量，我们构造了一个单参数全局解族。我们证明这些解对于实参数的所有值都是经典的，前提是方程中出现的差分算子符号的实部是正的。我们提出了一类满足这个条件的方程。