Exact Projective Excitations of a Generalized (3+1)-Dimensional Gross-Pitaevskii System with Varying Parameters




Jin-Xi Fei;Chun-Long Zheng

Key Words

Chinese Journal of Physics

Volume or Term/Year and Month of Publication

51卷2期(2013 / 04 / 01)

Page #

200 - 208

Content Language


English Abstract

An exact self-similar projective excitation for a generalized (3+1)-dimensional Gross-Pitaevskii system with time-modulated dispersion, nonlinearity, potential, and gain or loss is successfully derived with the aid of a direct projective approach. All the allowed exact solutions of the self-similarity projective equation can be converted into the corresponding exact solutions of the generalized Gross-Pitaevskii system under certain compatibility conditions. According to the derived projective solutions, some localized excitations with novel dynamical behavior are revealed by selecting appropriate system parameters. The integrable constraint condition for the generalized (3+1)-dimensional Gross-Pitaevskii system are first derived naturally.

Topic Category 基礎與應用科學 > 物理
  1. G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, (Cambridge University Press, Cambridge, 1996), Chap. 2.
  2. C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Phys. Rev. Lett. 19, 1095 (1967).
  3. R. Hirota, J. Math. Phys. 14, 810 (1973).
  4. R. M. Miura, Backlund Transformations,The Inverse Scattering Method, Solitons, and their Applications, Vol 515 in Lecture Notes in Mathematics, (Springer-Verlag, Berlin, 1976), Chap.5
  5. C. Q. Dai and J. F. Zhang, Int. Mod. Phys. B 19, 2129 (2005).
  6. S. K. Liu, Q. Zhao, and S. D. Liu, Chin. Phys. B 20, 040202 (2011).
  7. Z. Yang, S. H. Ma, and J. P. Fang, Chin. Phys. B 20, 040301 (2011).
  8. J. X. Fei and C. L. Zheng, Chin. Phys. B 21, 070304 (2012).
  9. J. X. Fei and C. L. Zheng, Z. Naturforsch. 66a, 1 (2011).
  10. H. Y. Wu, J. X. Fei, and C. L. Zheng, Commun. Theor. Phys. 54, 55 (2010).
  11. F. Brezzi and P. A. Markowich, Math. Meth. Appl. Sci. 14, 35 (1991).
  12. A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).
  13. C. L. Zheng and Y. Lin, Chin. Phys. B 21, 070305 (2012).
  14. Y. Gao and S. Y. Lou, Commun. Theor. Phys. 52, 1031 (2009).
  15. C. L. Zheng and L. Q. Chen, Int. J. Mod. Phys. B 22, 671 (2008).
  16. C. Dai, R. Chen, and Y. Wang, Chin. Phys. B 21, 030508 (2012)
  17. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman and Hall, London, 1997), Chap. 1.
  18. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, (Academic Press, New York, 2003), Chap. 1.
  19. F. Cariello and M. Tabor, Physica D 53, 59 (1991).
  20. B. Q. Li, Y. L. Ma, C. Wang, P. M. Xu, and Y. Li, Acta. Phys. Sin. 60, 060203 (2011).
  21. F. Dalfovo, S. Giorgini, L. P. Pitaesvkii, and S. stringari, Rev. Mod. Phys. 71, 463 (1999).
  22. C. Sulem and P. Sulem, The Nonlinear Schrodinger Equation: Self-Focusing and Wave collapse, (Springer-Verlag, Berlin, 2000), Chap. 6.
  23. F. K. Abdulaev, A. Gammal, L. Tomio, and T. Frederico, Phys. Rev. A 63, 043604 (2001).