Space-time chaos in the nonlinear Schrödinger equation

Abstract

Abstract The paper provides an analytical and numerical analysis of the transition to space-time chaos in the generalized nonlinear Schrödinger equation with complex, in the general case, parameters. Equation describes, in particular, the wave amplitude of a surface plasmon polariton propagating over the contact surface of a metal with a dielectric. It is proved that considered equation has an infinite number of different stable wave solutions running along the spatial axis with arbitrary velocities, as well as an infinite number of different modes of space-time chaos in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory. In this case, the bifurcation parameter is the value of the speed of propagation of traveling waves along the spatial axis, which is clearly not included in the original equation.