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Bright and dark soliton solutions and Bäcklund transformation for the Eckhaus–Kundu equation with the cubic–quintic nonlinearity

Author

Listed:
  • Wang, Pan
  • Tian, Bo
  • Sun, Kun
  • Qi, Feng-Hua

Abstract

In this paper, with symbolic computation, the Eckhaus–Kundu equation which appears in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics, is studied via the Hirota method. By virtue of the dependent variable transformation, the bilinear form is obtained. Bilinear Bäcklund transformation is given with the help of exchange formulae and the corresponding one-soliton solution is derived. Bright and dark N-soliton solutions are obtained. Propagation and interaction of the bright and dark solitons are discussed analytically and graphically. Interactions of the two solitons are presented. Bound state of the two solitons can be suppressed via the choice of parameters.

Suggested Citation

  • Wang, Pan & Tian, Bo & Sun, Kun & Qi, Feng-Hua, 2015. "Bright and dark soliton solutions and Bäcklund transformation for the Eckhaus–Kundu equation with the cubic–quintic nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 233-242.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:233-242
    DOI: 10.1016/j.amc.2014.11.014
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    References listed on IDEAS

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    1. Zhu, Shun-dong, 2007. "Exact solutions for the high-order dispersive cubic-quintic nonlinear Schrödinger equation by the extended hyperbolic auxiliary equation method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1608-1612.
    2. Triki, Houria & Taha, Thiab R., 2009. "Exact analytic solitary wave solutions for the RKL model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 849-854.
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