Related papers: Wave-by-wave forecasts in directional seas using n…

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…

Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of…

We analyze nonlinear guided waves in a planar waveguide made of a left-handed material surrounded by a Kerr-like nonlinear dielectric. We predict that such a waveguide can support fast and slow symmetric and antisymmetric nonlinear modes.…

Driven by the need for describing and understanding wave propagation in structural materials and components, several analytical, numerical, and experimental techniques have been developed to obtain dispersion curves. Accurate…

Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…

The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…

Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…

Reliable dynamic sea level forecasts are hindered by numerous sources of uncertainty on daily-to-seasonal timescales (1-180 days) due to atmospheric boundary conditions and internal ocean variability. Studies have demonstrated that certain…

In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…

Short-term forecasting is an important tool in understanding environmental processes. In this paper, we incorporate machine learning algorithms into a conditional distribution estimator for the purposes of forecasting tropical cyclone…

Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially,…

The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…

Process of the nonlinear deformation of the surface wave in shallow water is studied. Main attention is paid to the relation between the Fourier-spectrum and wave steepness. It is shown that the spectral harmonics of the initially sine wave…

In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…

Optical instruments for measuring surface-wave characteristics provide a better spatial and temporal resolution than other methods, but they face difficulties while converting the results of indirect measurements into absolute levels of the…