非交换BKP和CKP方程族的达布变换及其附加对称

发布时间：2018-05-26 16:06

  本文选题：达布变换 + 非交换BKP方程族　； 参考：《宁波大学》2017年硕士论文

【摘要】：在本篇文章中,我们给出了非交换B型Kadomtsev-Petviashvili(ncBKP)和非交换C型Kadomtsev-Petviashvili(ncCKP)方程族的定义,然后我们构造了ncBKP和ncCKP方程族的达布变换.从以上达布变换中,我们可以清楚地了解BKP方程族(或CKP方程族)和ncBKP方程族(或ncCKP方程族)的明显不同.除此之外,我们定义了ncBKP和ncCKP方程族的附加流,然后附加对称流将会构成一个无穷维李代数W_(1+∞).另外,附加对称的生成函数可以用波函数来表示,更进一步的是,我们在最后会得到ncBKP和ncCKP方程族的弦方程.最后,我们给出了非交换约束CKP方程族的递归算子以及非交换约束KP和多分量非交换约束KP方程族的递归算子,以便我们在以后的研究过程中可以得到任意高阶流.
[Abstract]:In this article, we give the definition of non commutative B type Kadomtsev-Petviashvili (ncBKP) and non commutative C Kadomtsev-Petviashvili (ncCKP) equation family, then we construct the Da cloth transformation of ncBKP and ncCKP equation family. From the above Da cloth transformation, we can clearly understand the BKP equation family (or CKP equation family) and ncBKP equation family ( In addition, we define the additional flow of the ncBKP and the ncCKP equation family, and then the additional symmetric flow will form an infinitely dimensional Lie algebra W_ (1+ infinity). In addition, the additional symmetric generation function can be expressed by the wave function, and further, we will finally get the chords of the ncBKP and ncCKP equations. In the end, we give recursive operators of non commutative constrained CKP equation family and recursive operators of non commutative constraint KP and multicomponent non commutative constraint KP equation family, so that we can get any higher order stream in the future research process.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】

相关期刊论文 前3条

1 ;Additional symmetries of constrained CKP and BKP hierarchies[J];Science China(Mathematics);2011年02期

2 ;The determinant representation of the gauge transformation for the discrete KP hierarchy[J];Science China(Mathematics);2010年05期

3 ;THE DETERMINANT REPRESENTATION OF THE GAUGE TRANSFORMATION OPERATORS[J];Chinese Annals of Mathematics;2002年04期

，

本文编号：1937872