Publication: Dynamics of a Ø4 kink in the presence of strong potential fluctuations, dissipation, and boundaries
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1991-07-15
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American Physical Society
Abstract
We have carried out a number of simulations to study the dynamical behavior of kinks in
the ifJ4 model in the presence of strong fluctuations of its double-well potential. Our work
widens the computational and analytical knowledge of this system in four directions. First,
we describe in detail a numerical procedure that can be easily generalized to other stochastic,
soliton-bearing equations. We demonstrate that it exhibits consistency features never found in
previous research on nonlinear stochastic partial differential equations. Second, we fix the range
of validity of theoretical approaches based on secular perturbative expansions. We show how this
range depends on a combination of noise strength and duration. Third, we numerically study
the model beyond the applicability of analytical methods. We compute the main characteristics
of kink dynamics in this regime and discuss their stability under this random perturbation.
Finally, we introduce dissipation and boundaries in the dynamically disordered model. We
establish that the essential consequence of friction action is to soften the noise effects, while
boundaries give rise to a critical velocity below which kinks cannot enter the noisy zone.
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Physical Review A, vol. 44, n. 1, 15 july 1991. Pp. 1086-1103