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

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...

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Bibliographic Details
Published in:Applied mathematics and computation 2015-01, Vol.251, p.233-242
Main Authors: Wang, Pan, Tian, Bo, Sun, Kun, Qi, Feng-Hua
Format: Article
Language:English
Subjects:
Bäcklund transformation
Eckhaus–Kundu equation
Hirota method
Soliton solutions
Symbolic computation
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.11.014