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Abstract:In this article the problem of two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability is presented and Homotopy Perturbation Method are employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. Comparisons are made between the Numerical solution (NM) and the results of the He's Homotopy Perturbation Method (HPM). The results reveal that these methods are very effective and simple and can be applied for other nonlinear problems.

We demonstrate the manifestations of nonlinear features in magnetic dynamics and I–V characteristics of a φ0 Josephson junction in the ferromagnetic resonance region. We show that at small values of the system parameters damping, spin–orbit interaction, and Josephson-to-magnetic energy ratio, the magnetic dynamics is reduced to the dynamics of a scalar Duffing oscillator driven by the Josephson oscillations. The role of the increasing superconducting current in the resonance region is clarified. Shifting of the ferromagnetic resonant frequency and the reversal of its damping dependence due to nonlinearity are demonstrated by the full Landau–Lifshitz–Gilbert–Josephson system of equations and in its different approximations. Finally, we demonstrate the negative differential resistance in the I–V characteristics and its correlation with the fold-over effect.

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