This study is divided into two important axes; for the first one, a new symmetric analytical (approximate) solution to Duffing–Helmholtz oscillatory equation in terms of elementary functions derived. The obtained compared with numerical using 4th Range–Kutta (RK4) approach and exact that elliptic functions. As second axis, we consider time-delayed version same oscillator taking impact both forc...

We study the adiabatic density perturbation in the oscillating inflation, proposed by Damour and Mukhanov. The recent study of the cosmological perturbation during reheating shows that the adiabatic fluctuation behaves like as the perfect fluid and no significant amplification occurs on super-horizon scales. In the oscillating inflation, however, the accelerated expansion takes place during the...

In this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. Iteration perturbation method leads us to high accurate solution. Two different high nonlinear examples are also presented to show the application and accuracy of the presented method. The results are compared with analytical methods and with the numerical solution using Runge-Kutta m...

We present a method to construct symplecticity-preserving renormalization group maps by using the Liouville operator, and obtain correctly reduced symplectic maps describing their long-time behavior even when a resonant island chain appears. There has been a long history to study an asymptotic solution of Hamiltonian flows by means of singular perturbation methods such as the averaging method a...

This paper presents a perturbation method for computing the normal forms of resonant double Hopf bifurcations with the aid of a computer algebraic system. This technique, based on the method of multiple time scales, can be used to deal with general n-dimensional systems without the application of center manifold theory. Explicit iterative formulas have been derived for uniquely determining the ...

A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. To demonstrate the method, all of the experimentally observed rotational energies, with values of J almost up to 100, for the ground and first excited vibrational states of CO2 and for the ground vibrational states of N2O and of OCS are calculated. All coupling between vibration...

The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the meth...

Abstract The strongly nonlinear dynamics of taut strings, traveled by a force moving with uniform velocity, is analyzed. A change variable performed, which recasts the equations motion in terms linearized dynamic displacement, measured from quasi-static response. Under hypothesis load velocity far enough celerity string, system appears form linear PDEs whose coefficients are slowly time. Since ...

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The dictionaries and classification parameters are trained by a classification objective, and the sparse features are extracted by reducing a reconstruction loss...

Singular perturbation methods, such as the method of multiple scales and the method of matched asymptotic expansions, give series in a small parameter ε which are asymptotic but (usually) divergent. In this survey, we use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a ‘hyperasymptotic’ approximation. This adds a se...