Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 16 min ago
PreprintarXiv licencearXiv

Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions

  • Dan Dai
  • Han-Han Sheng
Open at sourcePDFDOICite

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.

Related

  1. Approximating the poles of a Painlevé V transcendent for the Fredholm determinant of the sine kernel
    Walter Van Assche
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Asymptotic analysis of a Fredholm determinant occurring in the description of the dynamical correlation functions of the Lieb--Liniger Bose gas
    Frank Göhmann, Karol K. Kozlowski, Mikhail D. Minin
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXivHAL
  3. Isospectral and not strongly isospectral spherical space forms with non-cyclic fundamental group
    Mauro Colantonio
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Networks with Memory and Isospectral Reduction
    Grant Molnar
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. On isospectral potentials on periodic discrete graphs
    Natalia Saburova
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{dai2026fredholm,
  title = {{Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions}},
  author = {Dan Dai and Han-Han Sheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37421},
  eprint = {2609.37421},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37421},
}
RIS
TY  - UNPB
TI  - Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions
AU  - Dan Dai
AU  - Han-Han Sheng
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37421
UR  - https://arxiv.org/abs/2609.37421
AB  - 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.
ER  -