Аннотация:Analytical solutions are obtained for two problems for a discrete analogue of the Helmholtz equation
on a triangular lattice: (1) the problem of radiation from a point source on a plane; (2) the problem of
diffraction on a half-line with Dirichlet boundary conditions. It is shown that in these problems, the complete
field can be represented as an integral of an algebraic function over a family of contours located on some complex
manifold. The solution to the first problem is found as an integral of some differential form over this
manifold, and the asymptotics of the far field for this solution is obtained. The second problem is solved using
an analogue of the Sommerfeld integral. It is checked that the obtained solution coincides with the solution
of this problem by the Wiener–Hopf method.