in the present work, the effect of fluid’s elasticity was investigated on the hydrodynamic instability of blasius flow. to determine the critical reynolds number as a function of the elasticity number, a two-dimensional linear temporal stability analysis was invoked. the viscoelastic fluid is assumed to obey the walters’ b fluid model for which base flow velocity profiles were fortunately avail...

We consider the Cauchy problem for generalized Fornberg–Whitham equation with dissipation. This is one of nonlinear, nonlocal and dispersive-dissipative equations. The main topic this paper an asymptotic analysis solutions to problem. prove that solution converges modified heat kernel. Moreover, we construct second term asymptotics depending on degree nonlinearity. In view those profiles, inves...

The propagation of solitons in transmission lines periodically loaded with nonlinear capacitors is analyzed. It is demonstrated that the dependence of soliton amplitude on propagating velocity can be computed with a simple equation, valid for any arbitrary nonlinear capacitance. By means of an approximation to the nonlinear reactance, an analytical expression that completely describes soliton p...

We consider the problem of stabilization of unstable “shock-like” equilibrium profiles of the viscous Burgers’ equation with actuation at the boundaries. These equilibria are not stabilizable (even locally) using the standard “radiation boundary condition.” Using a nonlinear spatially-scaled transformation (that employs three ingredients, of which one is the Hopf-Cole nonlinear integral transfo...

Optical vortex solitons in a defocusing saturable medium are analyzed in the framework of the (2 1 1)-dimensional generalized nonlinear Schrödinger equation. Stationary, radially symmetric localized solutions with nonvanishing asymptotics and a phase singularity (vortex solitons) are found numerically for the varying saturation parameter. Relaxation of some localized initial profiles (e.g., vor...

We study the propagation of nonlinear waves in layered nonlinear dielectric/linear dielectric/metal planar structures. We develop vector models that describe the light propagation in such configurations and allow us to obtain both one- and two-dimensional solutions. We compute the nonlinear dispersion relation and the field profiles, and estimate losses. We use our models to design realistic st...

This paper presents a radar target recognition method using kernel locally linear embedding (KLLE) and a kernel-based nonlinear representative and discriminative (KNRD) classifier. Locally linear embedding (LLE) is one of the representative manifold learning algorithms for dimensionality reduction. In this paper, LLE is extended by using kernel technique, which gives rises to the KLLE algorithm...

In this paper, an extension of the effective index method (EIM) to waveguiding structures containing ideal or saturable third-order nonlinear materials is presented. By applying separation of variables to the dominant field component, the complete problem is subdivided into two scalar problems in the lateral and transverse direction, as in the case of the normal EIM. Making use of the strong tr...

In this study, we analyzed the effects of nonlinear thermal radiation and induced magnetic field on steady two-dimensional incompressible flow of Jeffrey fluid flow past a stretching/shrinking surface in the presence of homogeneous-heterogeneous reactions. For physical relevance in this study we analyzed the behavior of homogeneous and heterogeneous profiles individually. The transformed govern...