Related papers: Standing waves in a counter-rotating vortex filame…

We consider solitary water waves on the vorticity flow in a two-dimensional channel of finite depth. The main object of study is a branch of solitary waves starting from a laminar flow and then approaching an extreme wave. We prove that…

We study traveling waves in a coordinate-free model of flame fronts. The flame front is the interface between the burnt and unburnt phases of a gas undergoing combustion. The front therefore moves in a preferred direction, as the unburnt…

A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating…

The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear…

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…

Numerical simulation has indicated that vortex structures can exist for a long time in the form of quantized filaments on arrays of coupled weakly dissipative nonlinear oscillators in a finite three-dimensional domain under a resonant…

In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…

The standing wave solution on an idealized mass spring system can be found using straight forward algebra. The solution is found when this system makes jump rope like rotations around an axis.The standing wave forms a constant shape in a…

The nonlinear evolution of current filaments generated by the Weibel-type filamentation instability is a topic of prime interest in space and laboratory plasma physics. In this paper, we investigate the stability of a stationary periodic…

We study the formation of steady waves in two-dimensional fluids under a current with mean velocity $c$ flowing over a periodic bottom. Using a formulation based on the Dirichlet-Neumann operator, we establish the unique continuation of a…

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch…

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…

The spectrum of electromagnetic waves in periodic linear structures, such as periodic waveguides or chains of microelements i.e. spheres, cavities, exhibit the sequence of stop bands for propagating waves. Breaking the translational…

The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy…

We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for…

We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the frequency of the standing waves is below the limiting frequency,…

We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We show stability estimates for an arc-shaped vortex filament,…

When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…

The problem of standing wave formation by superposing two counter-propagating whistler waves in an overdense plasma, studied recently by Sano et al. (Phys. Rev. E 100, 053205 (2019) and Phys. Rev. E 101, 013206 (2020)), has been revisited…

We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can…