相关论文: Instability of large solitary water waves

This paper considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is vacuum, and that the waves are acted upon by gravity with surface…

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…

We study the dynamic pressure in an irrotational solitary wave propagating at the surface of water over a flat bed, under the influence of gravity. We consider the nonlinear regime, that is, the case of waves of moderate to large amplitude.…

The traveling wave with the peaked profile arises in the limit of the family of traveling waves with the smooth profiles. We study the linear and nonlinear stability of the peaked traveling wave by using a local model for shallow water…

A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of…

We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…

The solitary wave problem at the free surface of a two-dimensional, infinitely-deep and irrotational flow of water, under the influence of gravity, is formulated as a nonlinear pseudodifferential equation. A Pohozaev identity is used to…

The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly…

In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow…

Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…

A new condition for the linear dissipative instability of the strong plane shock wave in an arbitrary medium is obtained. The instability of the shock is realized due to the flow instability behind its front, which is similar to the known…

We address Euler's equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profile. In agreement with the previous numerical results,…

We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term.…

We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are…

We study the flow of water waves over bathymetry that varies periodically along one direction. We derive a linearized, homogenized model and show that the periodic bathymetry induces an effective dispersion, distinct from the dispersion…

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…

In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…