Subharmonic Generation by Resonant Three‐Wave Interaction of Deep‐Water Capillary Waves

Subharmonic generation has been observed during the propagation of deep‐water capillary waves. The observations are shown to be in agreement with the theory of degenerate resonant noncollinear three‐wave interaction in a nonlinear, dispersive medium

Self‐Refraction of Nonlinear Capillary‐Gravity Waves

Self‐refraction effects have been observed during the propagation of deep‐water capillary‐gravity waves. The observations are shown to be in qualitative agreement with the theory of self‐focusing and defocusing in a cubically nonlinear medium in the presence of diffraction

Exact Decomposition of Cnoidal Waves into Associated Solitons

Starting from the Korteweg de Vries equation, a precise model is developed of the decomposition of cnoidal waves into associated solitons

Stability of Acoustic Nonlinear Dispersive Eigenmodes

In an earlier investigation, spectral evolution equations were derived for nonlinear dispersive propagation. For the special case of two harmonics, two eigenmodes were shown to exist, of which one is parametric in nature. In this paper we develop a general method of stability analysis and show that in the case of two eigenmodes their limit cycle behavior is in agreement with earlier results obtained by different, less general, methods. We will also discuss the relation of the nonlinear eignmodes to cnoidal waves and acoustic solitons

Design of a Topologically Dispersive Acoustic Soliton Tank

The design of a topologically dispersive acoustic soliton tank, in which KdV solitons of desired amplitudes and widths may be generated and propagated, is presented. A potential application of the system as a traveling wave lens in acousto‐optic beam deflectors is also mentioned

A Heuristic Guide to Nonlinear Dispersive Wave Equations and Soliton-Type Solutions

In this paper we present a heuristic way of constructing nonlinear dispersive equations that lead to soliton or soliton-type solutions. We assume only that a general knowledge of the dispersion relation of the system is known, together with some insight into the effect of nonlinearity on wave speed. We show that such knowledge is sufficient to derive most known soliton equations and thus to provide the engineer with a quick way to assess whether or not his particular system is likely to exhibit soliton behavior. Naturally, a more detailed description requires knowledge of the basic equations governing the system and special techniques to handle initial conditions. To that purpose we provide the reader with ample references which he may want to consult in order to augment the information gained by the method outlined in this paper

Nonlinear Echoes, Phase Conjugation, Time Reversal, and Electronic Holography

In this paper we review the experiments on nonlinear echo phenomena during the last three decades, from spin echoes to echoes in piezoelectric powders. We show how the common principle is one of a physical Fourier transform space in which time reversal is brought about through phase conjugation. It will be seen how this leads to intriguing applications in signal processing, signal storage, and electronic holography

Two-Dimensional Strong, Acousto-Optic Interaction between Arbitrary Light and Sound Profiles: A Fourier Transform Approach

A spatial Fourier transform approach is employed to investigate the acoustooptic interaction with cw, profiled sound and an incident light beam. Two coupled differential equations which describe the near Bragg interaction are derived in the spatial frequency domain. Since there is no analytic solution for these coupled equations, a well-known numerical technique, viz., the Range-Kutta method is used to solve the equations. Detailed numerical simulation, involving Fourier transforming the input light beam profile to calculate the spectra of the scattered light beams and, hence, their profiles in space using the inverse transform, are presented

Reflection and Collision of Solitary Wave Solutions of the Nonlinear Klein-Gordon Equation

The reflection of solitary wave solutions of the cubically nonlinear Klein-Gordon equation from rigid and nonrigid boundaries, and their mutual interaction are studied using finite-difference numerical techniques. The instability of these solutions is shown to be removed by incorporating a small amount of a fifth-order saturating nonlinearity in the system