The exact solutions to the Davey-Stewartson 1 equations are constructed to describe the development of a transversal solitary wave instability. Two types of plane dark soliton decays into two-dimensional solitary waves are found and analysed. It is also shown that the transversal instability of one-dimensional waveguides leads only to a shift of their drift velocity under the action of nonlocal...

In this paper, we investigate the transverse linear instability of one-dimensional solitary wave solutions of the coupled system of two-dimensional long-wave-short-wave interaction equations. We show that the one-dimensional solitary waves are linearly unstable to perturbations in the transverse direction if the coefficient of the term associated with transverse effects is negative. This transv...

We exploit nonlinearity in NbN superconducting stripline resonators, which originates from local thermal instability, for studying stochastic resonance. As the resonators are driven into instability, small amplitude modulation (AM) signals are amplified with the aid of injected white noise. Simulation results based on the equations of motion for the system yield a good agreement with the experi...

We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species a...

We investigate both numerically and analytically the convective instability of granular materials by two dimensional traffic equations. In the absence of vibrations traffic equations assume two distinctive classes of fixed bed solutions with either a spatially uniform or nonuniform density profile. The former one exists only when the function V (ρ) that monitors the relaxation of grains assumes...

In a previous paper [I. Bena, M. Malek Mansour, and F. Baras, Phys. Rev. E 59, 5503 (1999)] the statistical properties of linearized Kolmogorov flow were studied, using the formalism of fluctuating hydrodynamics. In this paper the nonlinear regime is considered, with emphasis on the statistical properties of the flow near the first instability. The normal form amplitude equation is derived for ...