In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the multi-stage homotopy perturbation method (MHPM). The MHPM is a technique adapted from the standard homotopy perturbation method (HPM) where standard HPM is converted into a hybrid numeric-analytic method called multistage homotopy perturbation method (HPM). The MHPM is tested for several exam...

In this paper, a lattice hydrodynamic model of four-way pedestrian traffic considering turning capacity is proposed. The stability conditions are obtained by analysis. mKdV equation derived using the reductive perturbation method nonlinear analysis, and corresponding density wave solutions obtained. results theoretical analysis verified detailed numerical simulation spatial-temporal patterns fl...

Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Korteweg-de Vries (KdV) equation. The effect of cold (hot) dusty plasma density nc (nh) and the charge num...

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from giv...

In this letter we describe a new and simple approach for modulating the electromagnetic wave propagating in a dielectric medium in the form of solitons by considering the torque developed between the induced dipoles in the medium and external field without taking into account the nonlinear Kerr effect. A reductive perturbation method deduces the Maxwell equation coupled with the Larmor equation...

We study the reversal of magnetization in an isotropic ferromagnetic film free from charges by exposing it to a circularly polarized electromagnetic (EM) field. The magnetization excitations obtained in the form of line and lump solitons of the completely integrable modified KP-II equation which is derived using a reductive perturbation method from the set of coupled Landau-Lifshitz and Maxwell...

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated th...

A systematic investigation has been made of ion-acoustic solitary waves in plasma consisting of cold positively and negatively charged ions, as well as nonthermal electrons. The basic features of the solitary waves are investigated by using the reductive perturbation method, which is valid for the small but finite amplitude waves. Computational investigations have been performed to examine the ...