Fredholm行列式解在修正KP层次和二维Toda晶格中的应用：等谱与非等谱约化
Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions
- City University of Hong Kong（香港城市大学）
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中文总结 AI 辅助
本文研究修正KP层次和二维Toda晶格的Fredholm行列式解，通过等谱约化构造了mKdV、修正Camassa-Holm和聚焦非线性薛定谔方程的解，并展示了非等谱约化得到变形Bessel行列式解。
中文摘要 AI 辅助
我们研究了修正Kadomtsev-Petviashvili (mKP)层次的前两个正成员和第一个负成员以及双线性二维Toda晶格(2DTL)方程的Fredholm行列式解。通过应用等谱约化，我们显式构造了修正Korteweg-de Vries (mKdV)方程、修正Camassa-Holm方程和聚焦非线性薛定谔方程的Fredholm行列式解。此外，我们证明了在非等谱情形下，从mKP和2DTL方程约化到非等谱负KdV方程所得到的解由变形Bessel行列式刻画。
英文摘要
We study Fredholm determinant solutions to the first two positive and the first negative members of the modified Kadomtsev-Petviashvili (mKP) hierarchy, together with the bilinear two-dimensional Toda lattice (2DTL) equation. By applying isospectral reductions, we explicitly construct Fredholm determinant solutions for the modified Korteweg-de Vries (mKdV), the modified Camassa-Holm, and the focusing nonlinear Schrödinger equations. Furthermore, we demonstrate that in the non-isospectral case, the reduction from the mKP and 2DTL equations to the non-isospectral negative KdV equation yields solutions characterized by the deformed Bessel determinant.
