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Seismic surface wave dispersion inversion is used widely to study the subsurface structure of the Earth. The dispersion property is usually measured by using frequency-phase velocity (f-c) analysis and by picking phase velocities from the…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
Dynamical systems can be modelled by partial differential equations and numerical computations are used everywhere in science and engineering. In this work, we investigate the performance of recurrent and convolutional deep neural network…
We study deep water ocean wind-driven waves in strait, with wind directed orthogonally to the shore, through exact Hasselmann equation. Despite of "dissipative" shores - we do not include any reflection from the coast lines - we show that…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
In this contribution we evaluate the impact of filtering techniques in enhancing the accuracy of forecasts of optical turbulence and atmospheric parameters critical for ground-based telescopes. These techniques make use of the data…
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At…
In this letter, we provide an experimental demonstration of amplitude-dependent dispersion tuning of surface acoustic waves interacting with nonlinear resonators. Leveraging the similarity between the dispersion properties of plate edge…
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear…
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially…
Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when…
The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes non-overturning waves.…
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with…
We consider the fundamental problem of learning linear predictors (i.e., separable datasets with zero margin) using neural networks with gradient flow or gradient descent. Under the assumption of spherically symmetric data distribution, we…
We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which…
We report experimental observations of two canonical surface wave patterns --- ship waves and ring waves --- skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with…
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…