Journal of East China Normal University(Natural Sc ›› 2007, Vol. 2007 ›› Issue (5): 54-61.

• Article • Previous Articles     Next Articles

3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)

ZHOU Zhen-chuan 1,2, ZHOU Zhen-jiang 2,3   

  1. 1. Department of Mathematics, Huangshan College, Huangshan Anhui 245041, China ; 2. Department of Computer Science and Technology, East China Normal University , Shanghai 200062, China ; 3. Department of Information Science, Nanjing College for Population Programme Management, Nanjing 210042, China
  • Received:2006-06-21 Revised:2006-10-09 Online:2007-09-25 Published:2007-09-25
  • Contact: ZHOU Zhen-chuan

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Abstract: The Lax pair of a 3×3 matrix spectral problem was
constructed and the hierarchy corresponding to this Lax pair was
also obtained. This hierarchy includes not only KdV and mKdV
equations but also high-order NLS equation. Besides, with the help
of the gauge transformation of spectral problem, the Darboux
transformation of this $3\times3$ matrix spectral problem was
deduced and its explicit solutions were given.

Key words: hierarchy, Darboux transformation, high-order NLS equation, Lax pair, hierarchy, Darboux transformation, high-order NLS equation

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