On the chaotic dynamics in two coupled partial differential equations for evolution of surface plasmon polaritons

In this paper two coupled (linear and nonlinear) equations are studied. These equations describe dynamics of surface plasmon polaritons at dielectric-metal-dielectric surfaces. Previously constructed bifurcation diagram of an analytical spatially homogeneous solution is refined and verified by direct simulations. Further research is conducted using numerical scheme based on spectral method. The 2/3 de-aliasing rule is used to cope with nonlinearity along with pseudo-spectral approach. An Andronov-Hopf bifurcation of a stable limit cycle and a period-doubling bifurcation of a stable limit torus were found. Floquet theory was applied to verify bifurcations.