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Chaos, solitons and fractals in the nonlinear Dirac equation. (English) Zbl 1136.35455
Summary: By means of the asymptotic perturbation (AP) method, analytical investigation of a nonlinear Dirac equation shows the existence of interacting coherent excitations such as the dromions, lumps, ring soliton solutions and breathers as well as instanton solutions. The interaction between the localized solutions are completely elastic, because they pass through each other and preserve their shapes and velocities, the only change being a phase shift. Finally, one may obtain approximate lower-dimensional chaotic patterns such as chaotic-chaotic patterns, periodic-chaotic patterns, chaotic line soliton patterns and chaotic dromion patterns, due to the possibility of selecting appropriately some arbitrary functions. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution.

35Q55NLS-like (nonlinear Schrödinger) equations
35Q51Soliton-like equations
Full Text: DOI
[1] Lam, L.: Introduction to nonlinear physics. (1997) · Zbl 0974.00042
[2] Schroeder, M.: Fractals, chaos, power laws. (2000) · Zbl 0758.58001
[3] Infeld, E.; Rowlands, N.: Nonlinear waves, solitons and chaos. (1992) · Zbl 0994.76001
[4] Filippov, A. T.: The versatile soliton. (2000) · Zbl 0955.35002
[5] Maccari, A.: J. plasma phys.. 60, 275 (1998)
[6] Maccari, A.: J. phys. A. 32, 693 (1990)
[7] Ablowitz, M. J.; Clarkson, P. A.: Solitons, nonlinear evolution equations and inverse scattering. (1990) · Zbl 0762.35001
[8] Matveev, V. B.; Salle, M. A.: Darboux transformations and solitons. (1991) · Zbl 0744.35045
[9] Olver, P. J.: Applications of Lie groups to differential equations. (1993) · Zbl 0785.58003
[10] Lou, S. -Y.; Tang, X. -Y.; Qian, X. -M.; Chen, C. -L.; Lin, J.; Zhang, S. -L.: Mod. phys. Lett. B. 16, 1075 (2002)
[11] Tang, X. -Y.; Lou, S. -Y.; Zhang, Y.: Phys. rev. E. 66, 46601 (2002)
[12] Zheng, C. -L.: Chin. J. Phys.. 41, 442 (2003)
[13] Lou, S. -Y.: J. phys. A. 28, 7227 (1995)
[14] Lou, S. -Y.: Phys. lett. A. 276, 1 (2000)
[15] Tang, X. -Y.; Lou, S. -Y.: Chaos solitons fractals. 14, 1451 (2002)
[16] Ranada, A. F.: A.o.barutquantum theory, groups, fields and particles. Quantum theory, groups, fields and particles (1982)
[17] Cazenave, T.; Vazquez, L.: Commun. math. Phys.. 105, 35 (1986)
[18] Merle, F.: J. differential equations. 74, 50 (1988) · Zbl 0696.35154
[19] Balabane, M.; Cazenave, T.; Douady, A.; Merle, F.: Commun. math. Phys.. 119, 153 (1988)
[20] Balabane, M.; Cazenave, T.; Vazquez, L.: Commun. math. Phys.. 133, 53 (1990)
[21] Esteban, M. J.; Séré, E.: Commun. math. Phys.. 171, 323 (1995)
[22] Esteban, M. J.; Séré, E.: Discrete continuous dynam. Syst.. 8, 381 (2002)
[23] Maccari, A.: Chaos solitons fractals. 15, 141 (2003) · Zbl 1048.35098
[24] Maccari, A.: J. math. Phys.. 38, 4151 (1997)