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REMARKS ON NONLINEAR DIRAC EQUATIONS IN ONE SPACE DIMENSION
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 Title & Authors
REMARKS ON NONLINEAR DIRAC EQUATIONS IN ONE SPACE DIMENSION
HUH, HYUNGJIN;
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 Abstract
This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).
 Keywords
nonlinear Dirac equations;global existence;finite time blow up;
 Language
English
 Cited by
 References
1.
D. Agueev and D. Pelinovsky, Modeling of wave resonances in low-contrast photonic crystals, SIAM J. Appl. Math. 65 (2005), no. 4, 1101-1129. crossref(new window)

2.
T. Candy, Global existence for an $L^2$ critical nonlinear Dirac equation in one dimension, Adv. Differential Equations 16 (2011), no. 7-8, 643-666.

3.
A. Contreras, D. Pelinovsky, and Y. Shimabukuro, $L^2$ orbital stability of Dirac solitons in the massive Thirring model, arXiv:1312.1019.

4.
V. Delgado, Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac and other nonlinear Dirac equations in one space dimension, Proc. Amer. Math. Soc. 69 (1978), no. 2, 289-296. crossref(new window)

5.
R. H. Goodman, M. I. Weinstein, and P. J. Holmes, Nonlinear propagation of light in one-dimensional periodic structures, J. Nonlinear Sci. 11 (2001), no. 2, 123-168. crossref(new window)

6.
L. Haddad, C. Weaver, and L. Carr, The nonlinear Dirac equations in Bose-Einstein condensates: I. Relativistic solitons in armchair and zigzag geometries, arxiv:1305.6532v2.

7.
H. Huh, Global strong solution to the Thirring model in critical space, J. Math. Anal. Appl. 381 (2011), no. 2, 513-520. crossref(new window)

8.
H. Huh, Global strong solutions to some nonlinear Dirac equations in super-critical space, Abstr. Appl. Anal. (2013), Art. ID 602753, 8 pp.

9.
H. Huh, Global solutions to Gross-Neveu equation, Lett. Math. Phys. 103 (2013), no. 8, 927-931. crossref(new window)

10.
H. Huh and B. Moon, Low regularity well-posedness for Gross-Neveu equations, Comm. Pure Appl. Anal. 14 (2015), no. 5, 1903-1913. crossref(new window)

11.
D. Pelinovsky, Survey on global existence in the nonlinear Dirac equations in one spatial dimension, Harmonic analysis and nonlinear partial differential equations, 37-50, RIMS Kokyuroku Bessatsu, B26, Kyoto, 2011.

12.
D. Pelinovsky and Y. Shimabukuro, Orbital stability of Dirac solitons, Lett. Math. Phys. 104 (2014), no. 1, 21-41. crossref(new window)

13.
S. Selberg and A. Tesfahun, Low regularity well-posedness for some nonlinear Dirac equations in one space dimension, Differential Integral Equations, 23 (2010), no. 3-4, 265-278.

14.
J. Stubbe, Exact localized solutions of a family of two-dimensional nonlinear spinor fields, J. Math. Phys. 27 (1986), no. 10, 2561-2567. crossref(new window)

15.
Y. Zhang, Global strong solution to a nonlinear Dirac type equation in one dimension, Nonlinear Anal. 80 (2013), 150-155. crossref(new window)