Related papers: Modulational stability of nonlinear saturated grav…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
A nonlinear Schr\"odinger equation for the envelope of two-dimensional gravity-capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity-capillary…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
For low enough flow rates, turbulent channel flow displays spatial modulations of large wavelengths. This phenomenon has recently been interpreted as a linear instability of the turbulent flow. We question here the ability of linear…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
The search for solutions to the theory of weakly non-linear internal gravity wave turbulence is an active research topic. It is notably stimulated by the fact that this regime could drive fine-scale ocean dynamics for which the…
The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long range correlations, which behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We calculate the…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert-Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency…
The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different…
In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…
A flat-plate laminar boundary layer is simulated at Mach 6 and unit Reynolds number of 1.1e7 using the Direct Simulation Monte Carlo (DSMC) method to capture and analyze spontaneous second-mode instability growth. Power spectral density…
Possible dark states could be induced after derivations of the entrainment of matter induced by a surface wave propagating along the flexible vacuum-matter boundary by considering the nonlinear coupling between the interface and the…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…
We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…