Related papers: Nonlinear Density Waves in the Single-Wave Model
In this paper we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfv\'en, and fast wave eigenmodes, and…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
Collisionless regime kinetic models for coherent nonlinear Alfven wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term…
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…
Hydroelastic solitary waves propagating on the surface of a three-dimensional ideal fluid through the deformation of an elastic sheet are studied. The problem is investigated based on a Benney-Luke-type equation derived via an explicit…
We study the formation of large-scale coherent structures (a condensate) for a system of two weakly interacting classical waves. Using the coupled defocusing nonlinear Schr\"odinger (NLS) equations as a representative model, we focus on…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
The Rosensweig instability has a special character among the frequently discussed instabilities. One distinct property is the necessary presence of a deformable surface, and another very important fact is, that the driving force acts purely…
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases…
In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. As an application, we prove the existence of non-symmetric…
The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic equation. In the usual kinetic limit, the resulting…
We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential…
In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid…
We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond to harmonic forcing. This approach reconciles the…
Building on the Radon transform of the Vlasov-Poisson equations, a macroscopic fluid model for the coherent beam-beam interaction has been developed. It is shown that the Vlasov equation, expressed in action-angle variables, can be reduced…
Properties of solitary waves in pre-compressed Hertzian chains of particles are studied in the long wavelength limit using a well-known continuum model. Several main results are obtained by parameterizing the solitary waves in terms of…