Discovery of a nonpropagating hydrodynamic soliton

A new type water-surface-wave soliton, nonpropagating hydrodynamic soliton, was discovered. This is a self-trapped, highly localized, and stationary transverse water surface wave excitation which appears in a rectangular cross section resonator continuously excited parametrically by vertical oscillation. An experimental designed to create the soliton and the features of the soliton are described. The profiles of the soliton for various frequencies and amplitudes are measured. It is found that the profile of the soliton is accurately given by a hyperbolic secant function. The stability region that is the amplitude and frequency range of the drive in which individual soliton can be created without hysteresis is experimentally determined. The interaction between two solitons was investigated. It is observed that an attractive force exists between two solitons with the same polarity and a repulsive force exists between two solitons with the opposite polarity. The self-trapping mechanism of the soliton is studied. It is found that the necessary condition for creating the soliton is that the nonlinear dispersive system has an amplitude dependent resonant frequency of the transverse made such that the higher the amplitude the lower the resonant frequency. The soliton free decay rate was also measured. It was found that the soliton initially decays much faster than the corresponding linear transverse mode, but has the same rate in the terminal decay