In the paper, the problem of propagation of waves generated by localized source on a two-dimensional lattice is studied. The discrete problem is reduced to a continuous Cauchy problem, and the answer for this problem is constructed using the modified Maslov’s canonical operator, including a neighborhood of the leading wave front. The strong and weak dispersion effects depending on the relationship between the step of the lattice and the size of the initial perturbation are analyzed.

中文翻译：

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二维格上线性波传播问题的渐近渐近性及修正的Maslov规范算子

在本文中，研究了由局部源产生的波在二维晶格上的传播问题。离散问题被简化为连续的柯西问题，并且使用改进的Maslov规范运算符（包括前导波阵面的邻域）构造了该问题的答案。分析了取决于晶格步长和初始扰动大小之间关系的强和弱色散效应。