Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity
Here, 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 $$\mathcal{f(x) = r}$$ cos(Kx), 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 λ = 2π/K , and the soliton width $$l_s$$, which is a function of the nonlinearity $$\kappa$$ as well as the initial frequency ω0 of the solitary wave, there is a transition (at fixed ω0) from trapped to unbound behavior of the soliton, which depends on the parameters $$\mathcal{r}$$ and K of the external force and the nonlinearity parameter $$\kappa$$. We previously studied this phenomena when $$\kappa$$ = 1 where we showed that for λ $$\gg l_s$$ the soliton oscillates in an effective potential, while forλ $$\ll l_s$$ 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 $$\mathcal{r}$$ and K when $$\kappa$$ = 1/2,1,2 at fixed value of the frequency ω0. Since the solitary wave gets narrower for fixed ω0 as a function of $$\kappa$$, we expect and indeed find that the regime where the solitary wave is trapped is extended as we increase $$\kappa$$.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program; Indian National Science Academy (INSA); Alexander von Humboldt Foundation; Ministerio de Economía y Competitividad (MINECO); Ministerio de Ciencia, Innovacion y Universidades of Spain
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1798118
- Report Number(s):
- LA-UR-19-29780; TRN: US2210651
- Journal Information:
- Journal of Physics. A, Mathematical and Theoretical, Vol. 53, Issue 7; ISSN 1751-8113
- Publisher:
- IOP PublishingCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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