Periodic solutions of high accuracy to the forced Duffing equation: Perturbation series in the forcing amplitude

Nonresonant Excitation of the Forced Duffing Equation

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

Existence of Periodic Solutions for the Duffing Equation with Impulses

from linguistics to literature: a linguistic approach to the study of linguistic deviations in the turkish divan of shahriar

chapter i provides an overview of structural linguistics and touches upon the saussurean dichotomies with the final goal of exploring their relevance to the stylistic studies of literature. to provide evidence for the singificance of the study, chapter ii deals with the controversial issue of linguistics and literature, and presents opposing views which, at the same time, have been central to t...

Classification of solutions of the forced periodic nonlinear Schrödinger equation

The integrable structure of the periodic one-dimensional nonlinear Schrödinger equation is utilized to gain insights regarding the perturbed near-integrable dynamics. After recalling the known results regarding the structure and stability of the unperturbed standing and travelling waves solutions, two new stability results are presented: (1) it is shown numerically that the stability of the ‘ou...

Counting periodic solutions of the forced pendulum equation

Let h be a holomorphic function with h(0) = 1. The number of zeros of h on a disk centered at the origin can be controlled by the maximum value of |h| on a larger disk. This is a classical result in complex analysis that is sometimes called Jensen’s inequality (see for instance [4]). In [2] Il’yashenko and Yakovenko applied this result together with the theory of conformal mappings to count the...