Three Is a Crowd: Solitary Waves in Photorefractive Media with Three Potential Wells

In this paper we analytically, numerically, and experimentally study the dynamics of waves in photorefractive media in the presence of a potential with three wells. The results contained herein are also immediately applicable to the study of Bose–Einstein condensates in the weak interaction limit. Motivated by the recent theoretical and experimental efforts in the case of two wells, we systematically analyze the ways in which the bifurcation analysis of steady states and the stability picture are modified in the presence of a third potential well. In particular, it is shown that the presence of a third well causes all bifurcations to be of saddle‐node type. Our analytical results are based on a Lyapunov–Schmidt reduction in the modes of the underlying linear problem. We corroborate the analytical predictions with numerical results which are based on fixed point methods. Finally, we illustrate how these findings may be related to experimental observations obtained in strontium‐barium‐niobate crystals.