Applied Mathematics and Mechanics

, Volume 33, Issue 12, pp 1583–1594 | Cite as

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

  • Jing-sun Yao (姚静荪)Email author
  • Cheng Ou-Yang (欧阳成)
  • Li-hua Chen (陈丽华)
  • Jia-qi Mo (莫嘉琪)


A class of nonlinear disturbed coupled Schrödinger systems is studied. The specific technique is used to relate the exact and approximate solutions. The corresponding typical coupled system is considered. An exact shock travelling solution is obtained by a mapping method. The travelling asymptotic solutions of the disturbed coupled Schrödinger system are then found with an approximate method.

Key words

Schrödinger system solitary wave asymptotic solution 

Chinese Library Classification


2010 Mathematics Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Parkes, E. J., Duffy, B. R., and Abbott, P. C. Some periodic and solitary travelling-wave solutions of the short-pulse equation. Chaos, Solitons and Fractals, 38(1), 154–159 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Sirendaoreji, J. S. Auxiliary equation method for solving nonlinear partial differential equations. Phys. Lett. A, 309(5–6), 387–396 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    McPhaden, M. J. and Zhang, D. Slowdown of the meridional overturning circulation in the upper Pacific Ocean. nature, 415(3), 603–608 (2002)CrossRefGoogle Scholar
  4. [4]
    Pan, L. S., Zou, W. M., and Yan, J. R. The theory of the perturbation for Landau-Ginzburg-Higgs equation (in Chinese). Acta Phys. Sin., 54(1), 1–5 (2005)zbMATHGoogle Scholar
  5. [5]
    Feng, G. L., Dai, X. G., Wang, A. H., and Chou, J. F. On numerical predictability in the chaos system (in Chinese). Acta Phys. Sin., 50(4), 606–611 (2001)Google Scholar
  6. [6]
    Liao, S. J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press Co., New York (2004)zbMATHGoogle Scholar
  7. [7]
    He, J. H. and Wu, X. H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitions and Fractals, 29(1), 108–113 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Ni, W. M. and Wei, J. C. On positive solution concentrating on spheres for the Gierer-Meinhardt system. Journal of Differential Equations, 221(1), 158–189 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Bartier, J. P. Global behavior of solutions of a reaction-diffusion equation with gradient absorption in unbounded domains. Asymptotic Analysis, 46(3–4), 325–347 (2006)MathSciNetzbMATHGoogle Scholar
  10. [10]
    Libre, J., da Silva, P. R., and Teixeira, M. A. Regularization of discontinuous vector fields on R 3 via singular perturbation. Journal of Dynamics and Differential Equations, 19(2), 309–331 (2007)MathSciNetCrossRefGoogle Scholar
  11. [11]
    Guarguaglini, F. R. and Natalini, R. Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena. Communication in Partial Differential Equations, 32(2), 163–189 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Mo, J. Q. Singular perturbation for a class of nonlinear reaction diffusion systems. Science in China, Ser. A, 32(11), 1306–1315 (1989)zbMATHGoogle Scholar
  13. [13]
    Mo, J. Q. Homotopic mapping solving method for gain fluency of laser pulse amplifier. Science in China, Ser. G, 39(5), 568–661 (2009)Google Scholar
  14. [14]
    Mo, J. Q., Lin, Y. H., and Lin, W. T. Approximate solution of sea-air oscillator for El Ei Niñ o-southern oscillation model (in Chinese). Acta Phys. Sin., 59(10), 6707–6711 (2010)Google Scholar
  15. [15]
    Mo, J. Q. and Lin, S. R. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation. Chin. Phys. B, 18(9), 3628–3631 (2009)CrossRefGoogle Scholar
  16. [16]
    Mo, J. Q. Solution of travelling wave for nonlinear disturbed long-wave system. Commun. Theor. Phys., 55(3), 387–390 (2011)MathSciNetCrossRefGoogle Scholar
  17. [17]
    Mo, J. Q. and Chen, X. F. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation. Chin. Phys. B, 19(10), 100203 (2010)CrossRefGoogle Scholar
  18. [18]
    Li, B. Q., Ma, Y., Wang, C., Xu, M. P., and Li, Y. G′/G-expansion method and novel fractal structures for high-dimensional nonlinear physical equation (in Chinese). Acta Phys. Sin., 60(63), 060203 (2011)Google Scholar
  19. [19]
    Barbu, L. and Morosanu, G. Singularly Perturbed Boundary-Value Problems, Birkhäuser Basel, Basel (2007)zbMATHGoogle Scholar
  20. [20]
    De Jager, E. M. and Jiang, F. R. The Theory of Singular Perturbation, North-Holland Publishing, Amsterdam (1996)Google Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jing-sun Yao (姚静荪)
    • 1
    Email author
  • Cheng Ou-Yang (欧阳成)
    • 2
  • Li-hua Chen (陈丽华)
    • 3
  • Jia-qi Mo (莫嘉琪)
    • 1
    • 2
  1. 1.Department of MathematicsAnhui Normal UniversityWuhuAnhui Province, P. R. China
  2. 2.Faculty of ScienceHuzhou Teacher CollegeHuzhouZhejiang Province, P. R. China
  3. 3.Department of Mathematics and Computer ScienceFuqing Branch of Fujian Normal UniversityFuqingFujian Province, P. R. China

Personalised recommendations