Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Dai, Dan, Sheng, Han-Han
Institution: City University of Hong Kong
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: City University of Hong Kong
Awards: G9000367073, G9000367108
OpenAlex ID: W7214952911