Nonstationary modes of a thin and curved waveguide in a multiray zone (the uniform asymptotics)

The propagation of nonstationary modes in a thin waveguide with variable properties is considered in case of a space-time caustics presence. A connection of the cut-off section with these caustics is revealed. The uniform asymptotical formulas in a multiray zone are obtained and their transformation into formulas of the geometrical optics out of the caustics neughbourhood is observed.