In this work, we consider varying aspects of the stability of periodic traveling wave solutions to nonlinear dispersive equations. In particular, we are interested in deriving universal geometric criterion for the stability of particular third order nonlinear dispersive PDE’s. We begin by studying the spectral stability of such solutions to the generalized Korteweg-de Vries (gKdV) equation. Usi...

The applicabilty of superconductors to antennas is examined. Potential implementations that are examined are superdirective arrays; electrically small antennas; tuning and matching of these two; high-gain millimeter-wavelength arrays; and kinetic inductance slow wave structures for array phasers and traveling wave array feeds. Superdirective arrays and small antennas will not benefit directly, ...

Previous studies in non-human primates (NHPs) have shown that beta oscillations (15-30 Hz) of local field potentials (LFPs) in the arm/hand areas of primary motor cortex (MI) propagate as traveling waves across the cortex. These waves exhibited two stereotypical features across animals and tasks: (1) The waves propagated in two dominant modal directions roughly 180° apart, and (2) their propaga...

In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries (gKdV) equation ut = uxxx + f(u)x. In particular, we derive sufficient conditions for such a solution to be orbitally stable in terms of the Hessian of the classical action of the corresponding traveling wave ordinary differential equatio...

Abstract: Two class of fractional type solutions of Riccati equation are constructed from its three known solutions. These fractional type solutions are used to propose an approach for constructing infinite number of exact traveling wave solutions of nonlinear evolution equations by means of the extended tanh–function method. The infinite number of exact traveling wave solutions of the long–sho...

The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by ...

In this paper we derive a lattice model with infinite distributed delay to describe the growth of a single-species population in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction. We consider the existence of traveling wave solutions when the birth rate is large enough that each patch can sustain a positive equilibrium. When the birth ...

In this paper, we study the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction–diffusion equation with delay ∂u (x, t) ∂t = d u (x, t)+ f ⎛ ⎝u (x, t) , ∞ ∫ −∞ h (x − y) u (y, t − τ) dy ⎞ ⎠. Under the monostable assumption, we show that there exists a minimal wave speed c∗ > 0, such that the equation has no traveling wave front for 0 < c < c∗ and a tr...

Recent studies suggest that wave motions of the tectorial membrane (TM) play a critical role in determining the frequency selectivity of hearing. However, frequency tuning is also thought to be limited by viscous loss in subtectorial fluid. Here, we analyze effects of this loss and other cochlear loads on TM traveling waves. Using a viscoelastic model, we demonstrate that hair bundle stiffness ...

We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. To find the traveling wave solutions we introduce an ansatz in which the wave speed depends on the underlying lattice as well as on time. For the case of spatially periodic diffusion we obtain analytic solutions for the traveling wave problem usin...