Whispering-gallery waves in a neighborhood of an inflection point of the boundary. Asymptotics of the wave field as $t\to\infty$

The asymptotics is constructed as $t\to\infty$ for the wave field generated by a whispering-gallery wave incident on an inflection point of the boundary. The asymptotics has ray character and is connected with the family of rays tangent to the convex part of the boundary beyond the point of inflection.