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This paper is devoted to the investigation of the existence and stability of strongly localized modes in discrete media in Salerno model by using linear analysis method. The regions of stability and instability are determined. Also the existence of localized modes for different values of parameters is shown numerically by homoclinic orbits intersection method.

We first review the known mathematical results concerning the KP type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations : blow-up versus long time behavior, stability and instability of solitary waves.

We consider the influence of adsorption kinetics on a longwave oscillatory instability in a layer of a binary liquid heated from below. It is shown that an advection of the adsorbed surfactant leads to a strong stabilization of the mode. Qualitative explanation of the numerical results is provided.

This paper considers the stability analysis of periodic Takagi-Sugeno fuzzy models. For this we use a switching Lyapunov function defined at the time instants when the subsystems switch. Using the developed conditions we are able to prove the stability of periodic TS systems where the local models or even the subsystems are unstable. The application of the conditions is illustrated on numerical...

It is argued that many non-extremal black branes exhibit a classical Gregory-Laflamme instability if, and only if, they are locally thermodynamically unstable. For some black branes, the Gregory-Laflamme instability must therefore disappear near extremality. For the black p-branes of the type II supergravity theories, the Gregory-Laflamme instability disappears near extremality for p = 1, 2, 4 ...

In this letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the relevant dimensionless groups is in striking agreement with the results of the numerical simulations of the original nonlinear evolution equations. This sugge...

Recent experiments show that shear-banded flows of semidilute wormlike micelles in Taylor-Couette geometry exhibit a flow instability in the form of Taylor-like vortices. Here we perform the nonaxisymmetric linear stability analysis of the diffusive Johnson-Segalman model of shear banding and show that the nature of this instability depends on the applied shear rate. For the experimentally rele...

Capillary electrophoresis techniques often involve ion-concentration shock waves in an electrolyte solution, propagating under the effect of an external electric field. These shock waves are characterized by self-sharpening gradients in ion concentrations and electrical conductivity that are collinear with the electric field. The coupling of electric field and fluid motion at the shock interfac...

In this paper, a semi-discrete Brusselator system is considered. The Turing instability theory analysis will be given for the model, then Turing instability conditions can be deduced combining linearization method and inner product technique. A series of numerical simulations of the system are performed in the Turing instability region, various patterns such as square, labyrinthine, spotlike pa...