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• W3100107826 abstract "The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $kappa$ is analyzed, when the external force is periodic in space and given by $f(x) =rcos(K x)$, both numerically and in a variational approximation using five collective coordinates (time dependent shape parameters of the wave function). Our variational approximation satisfies exactly the low-order moment equations. Because of competition between the spatial period of the external force $lambda=2 pi/K$, and the soliton width $l_s$, which is a function of the nonlinearity $kappa$ as well as the initial frequency $omega_0$ of the solitary wave, there is a transition (at fixed $omega_0$) from trapped to unbound behavior of the soliton, which depends on the parameters $r$ and $K$ of the external force and the nonlinearity parameter $kappa$. We previously studied this phenomena when $kappa=1$ (2019 J. Phys. A: Math. Theor. {bf 52} 285201) where we showed that for $lambda gg l_s$ the soliton oscillates in an effective potential, while for $lambda ll l_s$ it moves uniformly as a free particle. In this paper we focus on the $kappa$ dependence of the transition from oscillatory to particle behavior and explicitly compare the curves of the transition regime found in the collective coordinate approximation as a function of $r$ and $K$ when $kappa=1/2,1,2$ at fixed value of the frequency $omega_0$. Since the solitary wave gets narrower for fixed $omega_0$ as a function of $kappa$, we expect and indeed find that the regime where the solitary wave is trapped is extended as we increase $kappa$." @default.
• W3100107826 created "2020-11-23" @default.
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• W3100107826 date "2020-01-22" @default.
• W3100107826 modified "2023-09-26" @default.
• W3100107826 title "Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity" @default.
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• W3100107826 doi "https://doi.org/10.1088/1751-8121/ab60e7" @default.
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