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Solitary waves in the nonlinear Dirac equation in the presence of external driving forces

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
 [1];  [2];  [3];  [4];  [5];  [6]
  1. Univ. of Bayreuth (Germany). Inst. of Physics
  2. Santa Fe Inst. (SFI), Santa Fe, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division. Center for Nonlinear Studies
  3. Univ. of Seville (Spain). Dept. of Applied Physics I. Inst. of Mathematics of the Univ. of Seville (IMUS)
  4. Peking Univ., Beijing (China). School of Mathematical Sciences. LMAM
  5. Savitribai Phule Pune Univ., Pune (India). Physics Dept.
  6. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division. Center for Nonlinear Studies
+ Show Author Affiliations
In this paper, we consider the nonlinear Dirac (NLD) equation in (1 + 1) dimensions with scalar–scalar self interaction g2/κ + 1 (Ψ¯Ψ)κ + 1 in the presence of external forces as well as damping of the form f(x) - iμγ0Ψ, where both f and Ψ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent response of the solitary waves to these external forces. This approach predicts intrinsic oscillations of the solitary waves, i.e. the amplitude, width and phase all oscillate with the same frequency. The translational motion is also affected, because the soliton position oscillates around a mean trajectory. For κ = 1 we solve explicitly the CC equations of the variational approximation for slow moving solitary waves in a constant external force without damping and find reasonable agreement with solving numerically the CC equations. Finally, we then compare the results of the variational approximation with no damping with numerical simulations of the NLD equation for κ = 1, when the components of the external force are of the form fj = rj exp(–iΚx) and again find agreement if we take into account a certain linear excitation with specific wavenumber that is excited together with the intrinsic oscillations such that the momentum in a transformed NLD equation is conserved.
Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE; National Natural Science Foundation of China; Alexander von Humboldt Foundation (Germany); Ministry of Science and Innovation (Spain); Junta de Andalucia (Spain); Univ. of Seville (Spain); Dept. of Atomic Energy (India)
Contributing Organization:
Univ. of Bayreuth (Germany); Santa Fe Inst. (SFI), Santa Fe, NM (United States); Univ. of Seville (Spain); Peking Univ., Beijing (China); Savitribai Phule Pune Univ., Pune (India)
OSTI ID:
1325634
Alternate ID(s):
OSTI ID: 22877995
Report Number(s):
LA-UR--15-21438
Journal Information:
Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 6 Vol. 49; ISSN 1751-8113
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (6)

Exact stationary solutions of the parametrically driven and damped nonlinear Dirac equation journal September 2019
Dynamics of Dirac solitons in networks journal September 2018
Externally driven nonlinear Dirac equation revisited: theory and simulations journal March 2019
Length-scale competition in the parametrically driven nonlinear Dirac equation with a spatially periodic force journal June 2019
Nonlinear spinor field in isotropic space-time and dark energy models journal July 2016
Nonlinear Spinor field in isotropic space-time and dark energy models text January 2016

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