期刊文献+

一个不含谱参数的谱变换

A new spectral transformation without spectral parameter
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摘要 利用已建立的Lie代数构造了一类新的含复数的谱问题,再用一个不含谱参数的规范变换将该谱问题转化为著名的Zakharov-Shabat特征值问题,由此得到了新的位势函数与原来的位势函数间的代数运算关系,也就是说,如果取原来函数的某些特殊值作为种子解的话,则利用该规范变换就可得到新的精确解.最后,将该规范变换约化为非线性演化方程的达布变换. By using the known Lie algebras,a type of new spectral problem containing complex number is constructed,which turns to well-known Zakharov-Shabat eigenvalue problem by employing a gauge transformation without spectral parameter.It follows that the relations between new potential functions and the orginal ones are linked up.That is,if we get some special values of the orginal potential functions as seed solutions,then we could obtain new solutions on potential functions.Finally,the guage transformation obtained in this paper reduces to a Darboux transformation of nonlinear evolution equations.
作者 赵晶 齐丽娟
出处 《辽宁师范大学学报(自然科学版)》 CAS 2010年第2期146-151,共6页 Journal of Liaoning Normal University:Natural Science Edition
基金 国家自然科学基金项目(10371023)
关键词 LIE代数 规范变换 达布变换 Lie algebra guage transformation Darboux transformation
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参考文献9

  • 1ZHANG E TANG.A class of normal transformation of the eigenvalue problems[J].Journal of University of Science and Technology of China,1983:54.
  • 2LI Yi-shen,CHEN Deng-yuan.Transformation operators of nonlinear evolution equations[J].Acta Mathematica Sinica,1986,29(1):127.
  • 3LI Yi-shen.Three kinds of Darboux transformation for the evolution equations which connect with AKNS eigenvalue problem[J].Acta Mathematica Sinica,New Series,1987,3(2):143.
  • 4ZHANG Yu-feng,WANG Yan.A higher-dimensional Lie algebra and its decomposedsubalgebras[J].Phys Lett A,2006,360:92.
  • 5FAN En-gui Integrable evolution systems based on Gerdjikov-Ivanov equation,bi-Hamihonian structure,finite-dimensional integrable systems and N-fold Darboux transformation[J].J Math Phys,2000,41(11):7769.
  • 6FAN En-gui,ZHANG Yu-feng.Vector loop algebra and its applications to integrable system[J].Chaos,Solitons and Fractals,2006,28(6):966.
  • 7ZHANG Yu-Feng,GUO Fu-Kui.Matrix Lie Algebras and Integrable Couplings[J].Communications in Theoretical Physics,2006,46(5X):812-818. 被引量:8
  • 8赵晶,龚新波.多分量loop代数及其应用[J].辽宁师范大学学报(自然科学版),2008,31(1):34-36. 被引量:1
  • 9ZHANG Yu-feng,HON Y C.Hamiltonian structure of two integrable couplings of the modified AKNS hierarchy[J].Modern Phys Lett B,2007,21(30):2063.

二级参考文献23

  • 1张玉峰.一个Lie代数的子代数及其相关的两类Loop代数[J].数学学报(中文版),2005,48(1):141-152. 被引量:10
  • 2W.X. Ma and B. Fuchssteiner, Chaos, Solitons and Fractals 7 (1996) 1227.
  • 3W.X. Ma, Methods Appl, Anal. 7 (2000) 21.
  • 4W.X. Ma and B. Fuchssteiner, Phys. Lett. A 213 (1996)49.
  • 5W.X. Ma, Phys. Lett. A 316 (2003) 72.
  • 6F.K. Guo and Y.F. Zhang, Acta Phys. Sin. 51 (2002) 951(in Chinese).
  • 7E.G. Fan and Y.F. Zhang, Chaos, Solitons and Fractals 25 (2005) 425.
  • 8F.K.Guo and Y.F. Zhang, J. Math. Phys. 44 (2003) 5793.
  • 9Y.F. Zhang, Chaos, Solitons and Fractals 21 (2004) 305.
  • 10Y.F. Zhang, Phys. Lett. A 310 (2003) 19.

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