Synchronous Spatiotemporal Oscillation Between Two Parametrically Excited Bound States

The bound state is one of the elemental localized excitations in a parametrically driven systems. In the molecule-like structure, the two identical solitons can interact with each other as a classic “oscillator”. Here the dynamics of two interacting bound states is explored by both experiment and computation. The experiment reveals several important dynamical features, in particular, the polarity ordering rule that determines the stability of a compound structure, and the synchronization in the coupling pairs of opposite polarity which leads to a symmetric and harmonic spatiotemporal oscillation. All these interesting phenomena are numerically simulated with the parametrically driven, damped nonlinear Schröding equation, and their nonlinear dynamics is further concluded as a stability diagram in parameter space.