本文選題：達(dá)布變換 + 非交換BKP方程族�。� 參考：《寧波大學(xué)》2017年碩士論文

【摘要】：在本篇文章中,我們給出了非交換B型Kadomtsev-Petviashvili(ncBKP)和非交換C型Kadomtsev-Petviashvili(ncCKP)方程族的定義,然后我們構(gòu)造了ncBKP和ncCKP方程族的達(dá)布變換.從以上達(dá)布變換中,我們可以清楚地了解BKP方程族(或CKP方程族)和ncBKP方程族(或ncCKP方程族)的明顯不同.除此之外,我們定義了ncBKP和ncCKP方程族的附加流,然后附加對稱流將會構(gòu)成一個(gè)無窮維李代數(shù)W_(1+∞).另外,附加對稱的生成函數(shù)可以用波函數(shù)來表示,更進(jìn)一步的是,我們在最后會得到ncBKP和ncCKP方程族的弦方程.最后,我們給出了非交換約束CKP方程族的遞歸算子以及非交換約束KP和多分量非交換約束KP方程族的遞歸算子,以便我們在以后的研究過程中可以得到任意高階流.
[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.
【學(xué)位授予單位】：寧波大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

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

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本文編號：1937872