Observations of Nonpropagating Oscillatory Solitons.
Abstract
The observation and theoretical interpretation of various nonpropagating oscillatory solitons is reported. The experiments were performed in a parametrically driven pendulum lattice and in a parametrically driven channel of shallow liquid. In the pendulum lattice, kink and breather solitons were observed. In the channel the first observation of a kink in standing surface waves is reported. Solitons are structures of interest because they represent robust localized motions of a medium. A perturbative analysis of slowly varying modulations of waves in a dispersive nonlinear medium leads to a Nonlinear Schrodinger (NLS) equation which has soliton solutions. The NLS level equations are formulated for both pendulum lattice and surface wave motions. Depending upon the cutoff mode and the sign of the nonlinearity, the solitons can be breathers or kinks. Spatially periodic solutions can be cnoidal, snoidal, or dnoidal waves. Because the NLS equation is a leading order approximation which has the remarkable property of being exactly integrable, one can question whether solitons can exist in real systems. The steady state motions observed in the pendulum lattice and channel persist indefinitely, however. The lattice has a simple novel design that avoids the use of springs. Large amplitude soliton data agree well with an adjustable parameter theory. Small amplitude data deviate significantly from the theory due to nonuniformities. The response of this mesoscopic system as a function of drive parameters is extremely rich and has already been found to exhibit at least five basins of attraction that are characterized by localized modes. Some of these have the nature of NLS solitons and some display quasiperiodic selffocusing. The observed surface wave kink exists in the fundamental cross mode of the channel. A remarkable property of the kink in this system is the extreme sensitivity to nonuniformities, which cause the kink to drift. The large amplitude data significantly deviates from the noadjustableparameter theory. The observations suggest that a damped driven soliton is a more general property of nature than the leading order theory implies. Finally, transverse modulations of damped driven nonlinear standing waves are investigated, with both parametric and direct drives. A linear stability analysis of the resultant NLS equation has shown that some modulations are unstable.
 Publication:

Ph.D. Thesis
 Pub Date:
 August 1990
 Bibcode:
 1990PhDT........54D
 Keywords:

 Physics: Acoustics; Physics: Fluid and Plasma; Physics: General