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Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity | | Fred Cooper
; Avinash Khare
; Niurka R. Quintero
; Bernardo Sánchez-Rey
; Franz G. Mertens
; Avadh Saxena
; | | Date: |
30 Nov 2019 | | 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. {f 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
$kappa$. | | Source: | arXiv, 1912.0103 | | Services: | Forum | Review | PDF | Favorites | |
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