We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.

We study orbital stability of solitary waves of least energy for a nonlinear Kawahara type equation (Benney-Luke-Paumond) that models long water waves with small amplitude, from the analytic and numerical viewpoint. We use a second-order spectral scheme to approximate these solutions and illustrate their unstable behavior within a certain regime of wave velocity.

In this paper, the localized TM surface waves of a nonlinear self-focusingleft-handed slab sandwiched between a uniform medium and a one-dimensionalphotonic crystal (1D PC) is analytically investigated. Our method is based on the firstintegral of the nonlinear Maxwell's equations. For the TM surface waves, the presenceof two electric field components makes the analysis difficult. Therefore, we ...

Large in situ measured ship-induced depression waves (Bernoulli wakes) in the Malamocco–Marghera industrial channel of the Venice Lagoon are interpreted as long-living strongly nonlinear Riemann (simple) waves of depression. The properties of these depressions are numerically replicated using nonlinear shallow water theory and the CLAWPACK software. The further behaviour of measured depressions...

Axisymmetric pipeline transportation of oil and water is simulated numerically as an initial value problem. The simulations succeed in predicting the spatially periodic Stokes-like waves called bamboo waves, which have been documented in experiments of Bai, Chen and Joseph (1992) for upow. The numerical scheme is validated against linearized stability theory for perfect core-annular ow, and wea...

The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schrödinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It i...

Two-dimensional deep water waves and some problems in nonlinear optics can be described by various third order dispersive equations, modifying and generalizing the KdV as well as nonlinear Schrödinger equations. We classify all third order polynomials up to certain transformations and study the pointwise decay for the fundamental solutions, Z

We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space-resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve three-wave resonant interactions. By studying the solutions of the resonance conditions, we show that the nonlinear interaction is dominantly one dimensional and in...

LONG-TERM GOALS The feasibility of using focused shock waves for mine neutralization requires detailed understanding of nonlinear wave propagation in water. This project investigates several fundamental issues of nonlinear acoustics when the primary source configuration is a discrete array of intense sources. Questions addressed through the theoretical analysis and an experimental effort concer...