Related papers: Traveling waves for models of phase transitions of…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…
Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions…
The transition from two-dimensional to three-dimensional flows in a finite circular cylinder driven by an axially oscillating sidewall is explored in detail. The complete symmetry group of this flow, including a spatio-temporal symmetry…
We study the diffusive dynamics of the classical one-dimensional lattice model of mobile particles featuring the incoherent metallic state of the organic TTF-CA found in the vicinity of the neutral-ionic(NI)-transition. The particles are…
The existence of traveling and standing waves is investigated for chains of coupled pendula with periodic boundary conditions. The results are proven by applying topological methods to subspaces of symmetric solutions. The main advantage of…
Active liquid crystals exert nonequilibrium stresses on their surroundings through constant consumption of energy, giving rise to dynamical steady states not present in equilibrium. The paradigmatic example of an active liquid crystal is a…
We consider a diffusion model with limit cycle reaction functions, in the presence of convection. We select a set of functions derived from a realistic reaction model: the Schnakenberg equations. This resultant form is unsymmetrical. We…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational…
We describe the effect of interfaces on classical wave propagation through diffusing layered media. A series resistor model for wave energy transport is introduced and we derive a microscopic expression for the interface resistance.
We investigate nonlinear periodic and solitary two-dimensional rolling waves in a falling two-layer liquid film in the regime of non-zero Reynolds numbers. At any flow rate, a falling two-layer liquid film is known to be linearly unstable…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes…
We study the interface between a solid trapped within a bath of liquid by a suitably shaped non-uniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields or a surface template. We…
A coupled system composed of a Newtonian fluid located on a sinusoidally-forced elastic solid is studied analytically and numerically. The focus is on the transient evolution from the beginning of the forced oscillations and on the periodic…
In this work, we solve the Euler's equations for periodic waves travelling under a sheet of ice using a reformulation introduced in Ablowitz et al. (2006). These waves are referred to as flexural-gravity waves. We compare and contrast two…