Dynamic behaviour of a non-propagating soliton under a periodically modulated oscillation

Abstract

It has been found theoretically and experimentally that a non-propagating soliton in a small rectangular water tank manifests dynamic behaviour when subjected to a modulated oscillation. A modification of the cubic Schrödinger equation was generalized for this case and analysed by the inverse-scattering perturbation method. The problem was reduced to a lower-dimensional one, i.e. to a pair of first-order ordinary differential equations for the amplitude and phase of the soliton, which were solved numerically. It was found that the soliton executes multi-periodic and chaotic motions under the periodically modulated oscillation. Corresponding experiments were carried out and both qualitative and quantitative agreement was obtained for the phenomena predicted and the parameter ranges in which they occur.