Related papers: Steady periodic water waves under nonlinear elasti…
This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or…
We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation.…
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…
A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of…
We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external…
We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current…
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…
Process of the nonlinear deformation of the surface wave in shallow water is studied. Main attention is paid to the relation between the Fourier-spectrum and wave steepness. It is shown that the spectral harmonics of the initially sine wave…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
The problem of the stability of a nonlinear thermomagnetic wave with respect to small thermal and electromagnetic perturbations in hard superconductors was studied. It is shown that spatially bounded solutions may correspond only to the…
We consider stability of an elastic membrane being on the bottom of a uniform horizontal flow of an inviscid and incompressible fluid of finite depth with free surface. The membrane is simply supported at the leading and the trailing edges…
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…
Weakly nonlinear internal wave-wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover,…
In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling wave problem used both…
We investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the framework of small amplitude waves, we find the solutions of the…
The present contribution contains a quite extensive theory for the stability analysis of plane periodic waves of general Schr{\"o}dinger equations. On one hand, we put the one-dimensional theory, or in other words the stability theory for…
We show that periodic traveling waves with sufficiently small amplitudes of the Whitham equation, which incorporates the dispersion relation of surface water waves and the nonlinearity of the shallow water equations,are spectrally unstable…
In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic…