Related papers: A mathematical model for rogue waves using Saint-V…
We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in theta functions. Unlike solutions generated on the plane wave background, these solutions depict rogue waves emerging on elliptic function backgrounds.…
The double-periodic solutions of the focusing nonlinear Schrodinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues.…
A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…
We have adapted the anelastic spectral code of Barranco & Marcus (2006) to simulate a turbulent convective layer with the intention of studying the effectiveness of turbulent eddies in dissipating external shear (e.g. tides). We derive the…
We model a 3D turbulent fluid, evolving toward a statistical equilibrium, by adding to the equations for the mean field $(v, p)$ a term like $-\alpha \nabla\cdot(\ell(x) D v_t)$. This is of the Kelvin-Voigt form, where the Prandtl mixing…
The present study investigates a way to design dykes which can filter the wavelengths of ocean surface waves. This offers the possibility to achieve a structure that can attenuate waves associated with storm swell, without affecting…
We report optical fiber experiments allowing to investigate integrable turbulence in the focusing regime of the one dimensional nonlinear Schr\"odinger equation (1D-NLSE). Our experiments are very similar in their principle to water tank…
We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…
In this paper we consider fundamental processes of the disturbance and propagation of internal gravity waves in the ocean modeled as a vertically stratified, horizontally non-uniform, and non-stationary medium. We develop asymptotic methods…
We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the…
The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…
The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The…
The goal of this paper is to describe in mathematical terms the effect on the ocean circulation of a random stationary wind stress at the surface of the ocean. In order to avoid singular behaviour, non-resonance hypotheses are introduced,…
We report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the…
Stratified flows forced by internal waves similar to those obtained in the Coriolis platform (LEGI, Grenoble, France) \cite{Savaro2020} are studied by pseudospectral triply-periodic simulations. The experimental forcing mechanism consisting…
We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system…
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic…
We are interested in the existence of travelling waves for the Benjamin-Bona-Mahony equation on a network. First we construct an explicit wave, defined in $\mathbb{R}$. Then, we use this wave to derive some conditions on the coefficients…