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ZHOU Zhen-chuan, ZHOU Zhen-jiang. 3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (5): 54-61.
Citation:
ZHOU Zhen-chuan, ZHOU Zhen-jiang. 3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (5): 54-61.
ZHOU Zhen-chuan, ZHOU Zhen-jiang. 3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (5): 54-61.
Citation:
ZHOU Zhen-chuan, ZHOU Zhen-jiang. 3×3 Matrix Spectral Problem and Its Darboux Transformation(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (5): 54-61.
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.
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