Abstract
In this paper, we investigate the soliton solutions of a 4D nonlinear pure spinor fermionic model with forcing and damping under white noise to understand how the dynamic of soler solitons could be affected by external excitations. For this purpose, we simulate the evolution of their with the phase-plane analysis which is one of the most significant methods for investigating the behaviors of nonlinear systems when the methods for calculating analytical solution do not exist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
P. A. M. Dirac, “The quantum theory of the electron,” Proc. R. Soc. London (1928).
W. Heisenberg, “Zur Quantentheorie Nichtrenormierbarer Wellengleichungen,” Zs. Naturforsch. 9a, 292 (1954).
F. Gursey, “On a conform-invariant spinor wave equation,” Nuovo Cim. 3, 988 (1956).
F. Kortel, “On some solutions of gursey’s conformal-invariant spinor wave equation,” Nuovo Cim. 4, 210 (1956).
M. Soler, “Ciassical, stable, nonlinear spinor field with positive rest energy,” Phys. Rev. D 1, 2766 (1970).
M. S. Sagaltici, Master’s Thesis (Istanbul Univ., Inst. Sci., Istanbul, Turkey, 2004).
M. Dunajski, Solitons, Instantons, and Twistors (Oxford Univ. Press, New York, 2010).
E. J. Weinberg, Classical Solutions in Quantum Field Theory: Solitons and Instantons in High Energy Physics (Oxford Univ. Press, New York, 2012).
R. Rajaraman, Solitons and Instantons (Elsevier Science, North-Holland, 1982).
V. G. Makhankov, Soliton Phenomenology (Kluwer Academic, US, 1990).
R. Mancini, Op Amps For Everyone (Texas Instrum., 2002).
F. Aydogmus, “Numeric solutions of Dirac-Gursey spinor field equation under external gaussian white noise,” Fluctuat. Noise Lett. 15, 1650018 (2016).
N. D. Anh and N. N. Hieu, “The duffing oscillator under combined periodic andrandomexcitations,” Probab. Eng. Mech. 30, 27–36 (2012).
H. T. Zhu, “Stochastic response of vibro-impact duffing oscillators under external andparametric gaussian white noises,” J. Sound Vibr. 333, 954–961 (2014).
F. Aydogmus and E. Tosyali, “Numerical analysis of thirring model under white noise,” J. Phys.: Conf. Ser. 633, 012022 (2015).
R. L. Lang, “A stochastic complex model with random imaginary noise,” Nonlin. Dyn. 62, 561–565 (2010).
F. Aydogmus, “Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations,” J. Exp. Theor. Phys. 120, 210–216 (2015).
F. Aydogmus, “Chaos in a 4D dissipative nonlinear fermionic model,” J. Mod. Phys. C 26, 1550083 (2015).
F. Aydogmus, “Unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models,” J. Exp. Theor. Phys. 125, 719–727 (2017).
S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Avalon, New York, 2014).
R. C. Yates, “Cassinian curves,” in A Handbook on Curves and Their Properties (J. W. Edwards, Ann Arbor, MI, 1952), pp. 8–11.
J. A. Gonzalez, A. Bellorin, and L. E. Guerrero, “Internal modes of Sine-Gordon solitons in the presence of spatiotemporal perturbations,” Phys. Rev. E 65, 065601 (2012).
Funding
This work was supported by the Scientific Research Projects Coordination Unit of Istanbul University; Project no. FBA-2018-28954.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aydogmus, F. Soliton Dynamics in a 4D Nonlinear Spinor Field Model under White Noise. Phys. Part. Nuclei Lett. 16, 613–619 (2019). https://doi.org/10.1134/S1547477119060050
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477119060050