ЖЭТФ, Том 120,
стр. 1157 (Ноябрь 2001)
(Английский перевод - JETP,
Vol. 93, No 5,
доступен on-line на www.springer.com
Ovchinnikov Yu.N., Sigal I.M.
Поступила в редакцию: 23 Мая 2001
PACS: 63.10.+a, 42.65.Tg
We consider the problem of the wave propagation through a nonlinear medium. We derive a dynamical system that governs the behavior of standing (or solitary) waves. The form of this system alone suffices to understand the qualitative dependence of solutions of the original equation on the intensity of the incident wave. We solve this dynamical system in the leading order in the nonlinearity strength. We find multiple solutions of the original problem for a given incoming wave and turning points of these solutions as a function of the intensity of the wave. We briefly investigate stability of different branches. Our results yield analytic description of the optical bistability phenomenon.