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Abstract
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In this paper, a theoretical model of the autoresonance effect based on the pseudoparticle oscillation
in a classical potential well is presented. The underlying connection between the autoresonance effect
and the shock wave generation in fluid dynamics is revealed and effects of different parameters such
as the potential, damping, external force amplitude, and frequency variation on the phase-locking
effect are examined. We use the full nonlinear energy spectrum of oscillations in order to selectively
choose our start frequency for the autoresonance effect to occur. We also use an exponential chirping
mechanism instead of the linear one which is usually employed. We believe that the former chirping
mechanism is a more natural way of energy injection into the dynamical system and provides a more
effective approach with sufficient control on the phase locking stability and duration. It is shown that
the double sweeping of both driving force magnitude and frequency leads to dense large amplitude
wave packets which we call autoexcitons. These entities may be useful in instantaneous energy transport in fluids and heating of plasmas. The autoresonance effect with exponential chirping and variable
force amplitude is shown to be effective for weakly nonlinear Helmholtz and Duffing oscillators as
well as fully nonlinear Sagdeev potential of electron-ion plasma hydrodynamic models. The occurrence of phase locking and autoexciton formation is studied for driven ion acoustic waves in terms of
different plasma parameters and equation of state of ion fluid.
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