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

Journal Article · Tue Jan 05 00:00:00 EST 2016 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8113/49/6/065402· OSTI ID:1325634

Mertens, Franz G. ^[1]; Cooper, Fred ^[2]; Quintero, Niurka R. ^[3]; Shao, Sihong ^[4]; Khare, Avinash ^[5]; Saxena, Avadh ^[6]

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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

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 f_j = r_j 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 Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; National Natural Science Foundation of China (NSFC); 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)
• Grant/Contract Number: 11471025; 91330110; 11421101; SPA 1146358 STP; FIS2014-54497-P; FQM207; P06-FQM-01735; P09-FQM-4643
• OSTI ID: 1325634
• Report Number(s): LA-UR-15-21438
• Journal Information: Journal of Physics. A, Mathematical and Theoretical, Vol. 49, Issue 6; ISSN 1751-8113
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

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