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Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales…
Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and…
Diffusive acceleration at collisionless shock waves remains one of the most promising acceleration mechanisms for the description of the origin of cosmic rays at all energies. A crucial ingredient to be taken into account is the reaction of…
We propose the feed-forward perturbation-based nonlinearity compensation method using the received signal, which outperforms conventional decision-based ones and eliminates the need for decision feedback. Additionally, combining half-half…
A new inversion method for determining near-surface shear currents from a measured wave spectrum is introduced. The method is straightforward to implement and starts from the existing state-of-the-art technique of assigning effective depths…
Inhomogeneities in the wave field due to wave groups, currents, and shoaling among other ocean processes can affect the mean water level. In this work, the classical and unsolved problem of continuously computing the set-down and the…
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…
Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, 2D models commonly used for the Earth cannot be applied to extrasolar telluric planets…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
We calculate the rate of ocean waves energy dissipation due to whitecapping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve…
We study the applicability of the derivative nonlinear Schr\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a…
The popular choice of using a $direct$ forecasting scheme implies that the individual predictions do not contain information on cross-horizon dependence. However, this dependence is needed if the forecaster has to construct, based on…
In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
By means of a direct and constructive method based on the theory of semiglobal $C^2$ solution, the local exact boundary observability is shown for nonautonomous 1-D quasilinear wave equations. The essential difference between nonautonomous…
Although the two-layer quasi-geostrophic equations (2QGE) are a simplified model for the dynamics of a stratified, wind-driven ocean, their numerical simulation is still plagued by the need for high resolution to capture the full spectrum…
We describe the theory and present numerical evidence for a new type of nonlinear resonant interaction between gravity waves on the surface of deep water. The resonance constitutes a generalisation of the usual 'exact' resonance as we show…
Optimal frequency identification in astronomical datasets is crucial for variable star studies, exoplanet detection, and asteroseismology. Traditional period-finding methods often rely on specific parametric assumptions, employ binning…
Numerical models have long been used to understand geoscientific phenomena, including tidal currents, crucial for renewable energy production and coastal engineering. However, their computational cost hinders generating data of varying…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…