| Abstract: | Self-similar solutions describing the incidence of a uniform solitary wave on a semi-infinite linear trough are obtained on the basis of the nonlinear ray method 1]. Previously, in investigating the incidence of a wave on a trough 2] the conditions at the discontinuities present in the solutions were derived on the assumption that they are of low intensity. In the present study the use of the conditions at the discontinuities obtained by investigating soliton interaction 3–5] has made it possible to construct a series of new solutions and take into account wave reflection effects and the formation of a shadow zone beyond the trough. The types of solutions that occur are established in terms of the relations between the wave parameters and the relative depth of the trough. To ensure that self-similar solutions exist for all values of the parameters it was necessary to introduce a type of discontinuity not previously encountered 5–7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 102–107, July–August, 1987.The author wishes to thank A. G. Kulikovskii and A. A. Barmin for discussing the work. |
