Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated. Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and ...

We perform a theoretical investigation on the Goos-Häenchen shift (the lateral shift) in one-dimensional photonic crystals (1DPCs) containing left-handed (LH) metamaterials. The effect was studied by use of a Gaussian beam. We show that the giant lateral displacement is due to the localization of the electromagnetic wave which can be both positive and negative depending on the incidence angle o...

The chaotic self-generation of short solitary spin wave pulses has been observed for the first time. The pulses were produced from parametrically excited spin waves in an yttrium-iron-garnet film in an active feedback ring under conditions where both three-wave and four-wave parametric processes were allowed. The power-frequency spectrum was broadband and chaotic.

A simple method to generate and characterize a pure highly vibrationally excited azulene molecular beam is demonstrated. Azulene molecules initially excited to the S4 state by 266-nm UV photons reach high vibrationally excited levels of the ground electronic state upon rapid internal conversion from the S4 electronically excited state. VUV laser beams at 157 and 118 nm, respectively, are used t...

This paper is concerned with bifurcation and stability problems of non-linear systems. The attention is focused on parametrically excited non-linear vibrations. A comparison of C—L method with IHB technique is given on the study of local bifurcations. It is shown that the two methods give qualitatively equivalent bifurcation diagrams. ( 1998 Elsevier Science Ltd. All rights reserved

We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales 1:3.

Interacting surface waves, parametrically excited by two commensurate frequencies, yield a number of nonlinear states. Near the system's bicritical point, a state, highly disordered in space and time, results from competition between nonlinear states. Experimentally, this disordered state can be rapidly stabilized to a variety of nonlinear states via open-loop control with a small-amplitude thi...

We show that ripples on the surface of deep water which are driven parametrically by monochromatic vertical vibration represent ensembles of oscillating solitons, or quasiparticles, rather than waves. The horizontal mobility of oscillons determines the broadening of spectral lines and transitions from chaos to regular patterns. It is found that microscopic additions of proteins to water dramati...

Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond ...