We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these me...

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to ...

Observed crest speeds of maximally steep, breaking water waves are much slower than expected. Our fully nonlinear computations of unsteadily propagating deep water wave groups show that each wave crest approaching its maximum height slows down significantly and either breaks at this reduced speed, or accelerates forward unbroken. This previously noted crest slowdown behavior was validated as ge...

We report on nonlinear optical effects on phoxonic cavities based on hollow whispering gallery mode resonators pumped with a continuous wave laser. We observed stimulated scattering effects such as Brillouin and Raman, Kerr effects such as degenerated and non-degenerated four wave mixing, and dispersive wave generation. These effects happened concomitantly. Hollow resonators give rise to a very...

The onset of turbulence is one of the outstanding problems of theoretical physics [Landau & Lifshitz, 1987; Frisch, 1995]. A seminal contribution to this study was brought about by Ruelle and Takens, who described the onset of turbulence as a sequence of Hopf bifurcations yielding a chaotic attractor in the system phase space [Ruelle & Takens, 1971; Newhouse et al., 1978]. In spite of the recen...

We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce strongly inhomogeneous distribution of the floaters: density fluctuations grow exponentially with a small but finite exponent. We show that the exponent is of si...

Steep, short-crested waves, as well as a large variety of three-dimensional propagating wave patterns have been created in laboratory, utilizing a plunging half-cone. Monochromatic waves, over a range of frequencies and amplitudes through breaking and including soliton wave groups near resonance, have been observed and studied in a small wave flume. This monochromatic wavemaker creates complex ...

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable fo...

We consider the propagation of sine-Gordon kinks in a planar curved strip as a model of nonlinear wave propagation in curved wave guides. The homogeneous Neumann transverse boundary conditions, in the curvilinear coordinates, allow to assume a homogeneous kink solution. Using a simple collective variable approach based on the kink coordinate, we show that curved regions act as potential barrier...

The evolution of internal solitary waves (ISWs) propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evo...