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Soliton solution of the DNLS equation based on Hirota’s bilinear derivative transform

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Wuhan University Journal of Natural Sciences

Abstract

Based on the method of Hirota’s bilinear derivative transform, the derivative nonlinear Schrödinger equation with vanishing boundary condition has been directly solved. The one- and two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.

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Authors and Affiliations

  1. School of Physics and Technology, Wuhan University, Wuhan, 430072, Hubei, China

    Guoquan Zhou

  2. School of Physics, China University of Science and Technology, Hefei, 230026, Anhui, China

    Xintao Bi

Authors
  1. Guoquan Zhou
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  2. Xintao Bi
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Correspondence to Guoquan Zhou.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (10775105)

Biography: ZHOU Guoquan(1965–), male, Associate professor, Ph.D., research direction: nonlinear integrable equations and field theory.

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Zhou, G., Bi, X. Soliton solution of the DNLS equation based on Hirota’s bilinear derivative transform. Wuhan Univ. J. Nat. Sci. 14, 505–510 (2009). https://doi.org/10.1007/s11859-009-0609-7

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  • DOI: https://doi.org/10.1007/s11859-009-0609-7

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