AI 中文总结
研究通过引入拟普法夫式数学结构，基于其西尔维斯特恒等式开发西尔维斯特 - 穆塔尔变换，为穆塔尔可变换的可积系统如诺维科夫 - 韦谢洛夫方程等生成新解，并回顾经典变换及讨论新对象性质。
AI 中文摘要
本文引入了一种名为拟普法夫式的数学结构，它类似于拟行列式，用于非交换情形替代行列式。基于拟普法夫式的西尔维斯特恒等式，开发了一种新变换——西尔维斯特 - 穆塔尔变换，为如诺维科夫 - 韦谢洛夫方程和二维正弦 - 戈登方程等穆塔尔可变换的可积系统生成新解。还在拟普法夫式背景下简要回顾了经典穆塔尔变换并讨论了新对象的其他性质。
英文摘要
In this paper, we introduce a mathematical structure called the quasiPfaffian. The quasiPfaffian is analogous to the quasideterminant, a structure used instead of a determinant in noncommutative settings. Building on the Sylvester identity for the quasiPfaffian, we develop a novel transformation, named the Sylvester Moutard transform, this generates new solutions for Moutard transformable integrable systems, such as the Novikov Veselov equation and the two dimensional sine Gordon equation. We also briefly review the classical Moutard transformation in the context of quasiPfaffians and discuss several additional properties of this new object.
Comments18 pages
