| Abstract: | A lot of attention has been paid to standing wave modes in nonlinear wave systems with localized structure (defects). In particular, applied mathematicians have been interested in the question of whether such modes are stable. Less attention has been paid to the dynamics that arise as the result of instability. In this talk, I discuss the conditions that give rise to oscillatory instabilities in a system of three parallel waveguides. I construct a family of waveguides in which simple solutions are unstable at arbitrarily small amplitudes. I show that above critical intensity, the light hops chaotically between the the three waveguides and discuss the implications of this for larger arrays of waveguides. |
