@misc{NIST2026DLMFBeta,
  author = {{National Institute of Standards and Technology}},
  title = {{NIST Digital Library of Mathematical Functions}: Beta Function and Gamma Recurrence},
  year = {2026},
  howpublished = {Online reference, version 1.2.8},
  note = {Released 2026-09-15; equations 5.12.1 and 5.5.1},
  url = {https://dlmf.nist.gov/5.12}
}

@misc{NIST2026DLMFElliptic,
  author = {{National Institute of Standards and Technology}},
  title = {{NIST Digital Library of Mathematical Functions}: Elliptic Integrals},
  year = {2026},
  howpublished = {Online reference, version 1.2.8},
  note = {Released 2026-09-15; equations 19.2.4, 19.2.8, 19.12.1 and 19.12.3},
  url = {https://dlmf.nist.gov/19.2}
}

@incollection{Aktosun2009IST,
  author = {Aktosun, Tuncay},
  title = {Inverse Scattering Transform and the Theory of Solitons},
  editor = {Meyers, Robert A.},
  booktitle = {Encyclopedia of Complexity and Systems Science},
  publisher = {Springer},
  pages = {4960--4971},
  year = {2009},
  doi = {10.1007/978-0-387-30440-3_295},
  eprint = {0905.4746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0905.4746v1},
  note = {Reading locators refer to arXiv v1}
}

@article{BlochKarp2023Toda,
  author = {Bloch, Anthony M. and Karp, Steven N.},
  title = {Symmetric Toda, gradient flows, and tridiagonalization},
  journal = {Physica D: Nonlinear Phenomena},
  volume = {450},
  pages = {133766},
  year = {2023},
  doi = {10.1016/j.physd.2023.133766},
  eprint = {2304.10697},
  archivePrefix = {arXiv},
  note = {Reading locators refer to arXiv v1}
}

@book{CannasDaSilva2001Symplectic,
  author = {Cannas da Silva, Ana},
  title = {Lectures on Symplectic Geometry},
  series = {Lecture Notes in Mathematics},
  volume = {1764},
  publisher = {Springer},
  year = {2001},
  doi = {10.1007/978-3-540-45330-7},
  note = {Author revision January 2006; cited page numbers refer to that revision},
  url = {https://people.math.ethz.ch/~acannas/Papers/lsg.pdf}
}

@article{Caux2009ABACUS,
  author = {Caux, Jean-Sébastien},
  title = {Correlation functions of integrable models: a description of the {ABACUS} algorithm},
  journal = {Journal of Mathematical Physics},
  volume = {50},
  pages = {095214},
  year = {2009},
  doi = {10.1063/1.3216474},
  eprint = {0908.1660},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0908.1660v1},
  note = {Reading locators refer to arXiv v1}
}

@article{CauxMossel2011Integrability,
  author = {Caux, Jean-Sébastien and Mossel, Jorn},
  title = {Remarks on the notion of quantum integrability},
  journal = {Journal of Statistical Mechanics: Theory and Experiment},
  year = {2011},
  pages = {P02023},
  doi = {10.1088/1742-5468/2011/02/P02023},
  eprint = {1012.3587},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1012.3587v1},
  note = {Reading locators refer to arXiv v1}
}

@misc{Faddeev1996ABA,
  author = {Faddeev, L. D.},
  eprint = {hep-th/9605187},
  title = {How Algebraic Bethe Ansatz works for integrable model},
  year = {1996},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/9605187v1},
  note = {Reading locators refer to arXiv v1}
}

@article{GolinelliMallick2004Gap,
  author = {Golinelli, Olivier and Mallick, Kirone},
  title = {Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {37},
  number = {10},
  pages = {3321--3331},
  year = {2004},
  doi = {10.1088/0305-4470/37/10/001},
  eprint = {cond-mat/0312371},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/0312371v1},
  note = {Reading locators refer to arXiv v1 PDF}
}

@article{GolinelliMallick2006ASEP,
  author = {Golinelli, Olivier and Mallick, Kirone},
  title = {The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {39},
  number = {41},
  pages = {12679--12705},
  year = {2006},
  doi = {10.1088/0305-4470/39/41/S03},
  eprint = {cond-mat/0611701},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/0611701v1},
  note = {Reading locators refer to arXiv v1 PDF}
}

@article{GrunertTeschl2009KdV,
  author = {Grunert, Katrin and Teschl, Gerald},
  title = {Long-time asymptotics for the {Korteweg--de Vries} equation via nonlinear steepest descent},
  journal = {Mathematical Physics, Analysis and Geometry},
  volume = {12},
  pages = {287--324},
  year = {2009},
  doi = {10.1007/s11040-009-9062-2},
  note = {Reading locators refer to the author PDF}
}

@misc{Hairer2010Symplectic,
  author = {Hairer, Ernst},
  title = {Geometric Numerical Integration, Lecture 2: Symplectic integrators},
  year = {2010},
  howpublished = {TU M{\"u}nchen lecture notes, January--February},
  url = {https://www.unige.ch/~hairer/poly_geoint/week2.pdf}
}

@article{Hoeffding1963Inequalities,
  author = {Hoeffding, Wassily},
  title = {Probability Inequalities for Sums of Bounded Random Variables},
  journal = {Journal of the American Statistical Association},
  volume = {58},
  number = {301},
  pages = {13--30},
  year = {1963},
  doi = {10.1080/01621459.1963.10500830}
}

@article{KarbachMuller1997Bethe,
  author = {Karbach, Michael and Müller, Gerhard},
  journal = {Computers in Physics},
  volume = {11},
  pages = {36--43},
  eprint = {cond-mat/9809162},
  title = {Introduction to the Bethe ansatz I},
  year = {1997},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9809162v1},
  note = {Reading locators refer to arXiv v1},
  doi = {10.1063/1.4822511}
}

@article{KassamTrefethen2005TimeStepping,
  author = {Kassam, Aly-Khan and Trefethen, Lloyd N.},
  title = {Fourth-order time-stepping for stiff {PDEs}},
  journal = {SIAM Journal on Scientific Computing},
  volume = {26},
  number = {4},
  pages = {1214--1233},
  year = {2005},
  doi = {10.1137/S1064827502410633}
}

@article{Lax1968Integrals,
  author = {Lax, Peter D.},
  title = {Integrals of nonlinear equations of evolution and solitary waves},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {21},
  pages = {467--490},
  year = {1968},
  doi = {10.1002/cpa.3160210503},
  note = {Reading locators refer to report NYO-1480-87, January 1968}
}

@incollection{Moser1975Toda,
  author = {Moser, J{\"u}rgen},
  title = {Finitely many mass points on the line under the influence of an exponential potential---an integrable system},
  editor = {Moser, J{\"u}rgen},
  booktitle = {Dynamical Systems, Theory and Applications},
  series = {Lecture Notes in Physics},
  volume = {38},
  pages = {467--497},
  publisher = {Springer},
  year = {1975},
  doi = {10.1007/3-540-07171-7_12}
}

@article{NepomechieWang2013Singular,
  author = {Nepomechie, Rafael I. and Wang, Chunguang},
  title = {Algebraic Bethe ansatz for singular solutions},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {46},
  number = {32},
  pages = {325002},
  year = {2013},
  doi = {10.1088/1751-8113/46/32/325002},
  eprint = {1304.7978},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1304.7978v3},
  note = {Reading locators refer to arXiv v3 PDF}
}

@article{NepomechieWang2014Twisting,
  author = {Nepomechie, Rafael I. and Wang, Chunguang},
  title = {Twisting singular solutions of Bethe's equations},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {47},
  number = {50},
  pages = {505004},
  year = {2014},
  doi = {10.1088/1751-8113/47/50/505004},
  eprint = {1409.7382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1409.7382v3},
  note = {Reading locators refer to arXiv v3 PDF}
}

@misc{Preskill2015QuantumChapter2,
  author = {Preskill, John},
  title = {Lecture Notes for Ph219/CS219: Quantum Information, Chapter 2: Foundations I: States and Ensembles},
  year = {2015},
  howpublished = {California Institute of Technology lecture notes},
  note = {Updated July 2015},
  url = {https://www.preskill.caltech.edu/ph219/chap2_15.pdf}
}

@book{Teschl2012ODE,
  author = {Teschl, Gerald},
  title = {Ordinary Differential Equations and Dynamical Systems},
  series = {Graduate Studies in Mathematics},
  volume = {140},
  publisher = {American Mathematical Society},
  address = {Providence},
  year = {2012},
  isbn = {978-0-8218-8328-0},
  note = {Cited locators refer to the author preliminary PDF, preface dated April 2012},
  url = {https://www.mat.univie.ac.at/~gerald/ftp/book-ode/index.html},
  doi = {10.1090/gsm/140}
}

@misc{Torrielli2016Classical,
  author = {Torrielli, Alessandro},
  title = {Lectures on Classical Integrability},
  year = {2016},
  eprint = {1606.02946},
  archivePrefix = {arXiv},
  primaryClass = {hep-th},
  version = {1},
  url = {https://arxiv.org/abs/1606.02946v1}
}

@article{Wilson1927Inference,
  author = {Wilson, Edwin B.},
  title = {Probable Inference, the Law of Succession, and Statistical Inference},
  journal = {Journal of the American Statistical Association},
  volume = {22},
  number = {158},
  pages = {209--212},
  year = {1927},
  doi = {10.1080/01621459.1927.10502953}
}

@misc{Zung2018ActionAngle,
  author = {Zung, Nguyen Tien},
  title = {A conceptual approach to the problem of action-angle variables},
  year = {2018},
  eprint = {1706.08859},
  archivePrefix = {arXiv},
  primaryClass = {math.DS},
  version = {2},
  url = {https://arxiv.org/abs/1706.08859v2}
}