The integral sign with a backslash denotes the principal value. The constant σ is taken to be ±1. For positive (negative) σ, the equation is called the defocusing (focusing) INLS equation. Originally, the defocusing INLS equation was discovered by carrying out a reductive perturbation method for the ILW equation [8]. It describes the long–term evolution of quasi–harmonic wave packets whose wave...

A difference equation is presented to describe traffic flow on a highway. The difference equation model is derived from the optimal velocity models formulated in terms of the differential equations. It is compared with the differential equation models. We investigate phase transitions among the freely moving phase, the coexisting phase in which jams appear, and the uniform congested phase. The ...

In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly nonlinear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg–de Vries (KdV) equation. A progressive wave type of solution, which sati...

A dusty plasma system containing Boltzmann-distributed electrons, non-thermal ions, and mobile charge fluctuating negative dust has been considered. The nonlinear propagation of the dust-acoustic (DA) waves in such a dusty plasma has been investigated by employing the reductive perturbation method. It has been found that the dust charge fluctuation is a source of dissipation, and is responsible...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

In the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying j velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear S...

The microwave absorbing characteristics of magnetic separation products (magnetic and non-magnetic) of reductive products of ilmenite concentrate were measured by the method of microwave cavity perturbation and the magnetic separation products were characterized by X-Ray Diffraction (XRD). It was demonstrated that metallic iron was a strong microwave absorbing material, while TiO2 was a weak mi...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

in this paper, we try to use modeling based on singular perturbation theory, in order to control satellite attitude during the wide rolling angle maneuvering through nonlinear h∞ control strategy. differential equations describing dynamics of the satellite are presented first, and by choosing the appropriate dynamic model for actuators and based on the standard singular perturbation model, the ...