## 非交换可积方程族的精确解

The Exchange of Accurate Solution of Integrability Equation Family
Abstract: In the thesis, we study the exchange of accurate solution of integrability equation family of Lax integrability and some nonlinear evolution equations defined on noncommutative rings.Based on the theory of Lax integrability, several noncommutative integrable equations are obtained by extention of original Lax equation which include noncommutative AKNS equation, noncommutative coupling Harry-Dym equation,noncommutative Kaup-Newell(KN) equation,noncommutative Leci equation and noncommutative Toda lattice equation..In Chapter 1, we obtain the noncommutative isospectrum AKNS equation hierarchy through extention of Lax integrable system, considering with the coupling Harry-Dym (H-D) spectral problem, we calculate Lenard operators K, J and the Coupling H-D equation hierarchy from the noncommutation respectively,and the Kaup-Newell (KN) spectrum problem by a similar approach.In Chapter 2,we discusses about the commutative and noncommutative isospectrum Levi equation hierarchy.In Chapter 3, discusses about the reduction of the matrix Toda lattice equation by a similar approach.

Key words: AKNS Equation; Coupling H-D Equation; KN Equation ; Levi Equation; Toda lattice equation
目    录

1.几个非交换可积方程    6
1.1非交换等谱AKNS方程族    6
1.2非交换耦合Harry-Dym方程族     8
1.3非交换KN方程族    9
2.Levi方程    13
2.1 交换等谱Levi方程    13
2.2 非交换等谱Levi方程    16
3.等谱Toda链方程族    19
3.1等谱Toda链方程族    19
3.2 非交换等谱Toda链方程    22

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