Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-02-20
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 35 Pages, 8 figures
Scientific paper
Asymptotic methods in nonlinear dynamics are used usually to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann cosmological equations, not only small oscillations regime is of interest but also the regime of rolling (claiming), more precisely the rolling from a top (claiming to the top). In the Friedman cosmology, where the slow rolling regime is often used, the rolling from a top (not necessary slow) is of interest too. In the present work a method for approximate solution to the Higgs equation in the rolling regime is presented. It is shown that in order to improve perturbation theory in the rolling regime it turns out to be effective not to use an expansion in trigonometric functions as it is done in case of small oscillations but use expansions in hyperbolic functions instead. This regime is investigated using the representation of the solution in terms of elliptic functions. An accuracy of the corresponding approximation is estimated.
Arefeva Ya. I.
Piskovskiy E. V.
Volovich Igor V.
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