Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (4): 1457-1464.doi: 10.1016/S0252-9602(11)60331-7

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DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS

 LI Wen-Min, HAN You-Qin, ZHOU Gao-Jun   

  1. College of Sciences, the Northwest Sci-Tech University of Agriculture and Forestry, Yangling 712100, China; College of Sciences, Xi’an Jiaotong University, Xi’an 710049, China; Department of Mathematics, Henan College of Education, Zhengzhou 450052, China
  • Received:2009-07-02 Revised:2009-12-25 Online:2011-07-20 Published:2011-07-20
  • Supported by:

    Project supported by the Talent Foundation of the Northwest Sci-Tech University of Agriculture and Forestry (01140407).

Abstract:

In this paper, we study a differential-difference equation associated with dis-crete 3 ×3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an appli-cation, explicit soliton solutions of the differential-difference equation are given.

Key words: Darboux transformation, solitons, explicit solution, Lax-pair, differential-difference equation

CLC Number: 

  • 35Q51
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