@book {BF,
    AUTHOR = {Byrd, Paul F. and Friedman, Morris D.},
     TITLE = {Handbook of elliptic integrals for engineers and physicists},
    SERIES = {Grundlehren Math. Wiss.},
    VOLUME = {67},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1954},
     PAGES = {xiii+355},
       DOI = {10.1007/978-3-642-52803-3},
       URL = {https://doi.org/10.1007/978-3-642-52803-3},
}

@article {CI99,
    AUTHOR = {Calini, Annalisa and Ivey, Thomas},
     TITLE = {Topology and sine-{G}ordon evolution of constant torsion curves},
   JOURNAL = {Phys. Lett.~A},
  FJOURNAL = {Physics Letters~A},
    VOLUME = {254},
      YEAR = {1999},
    NUMBER = {3--4},
     PAGES = {170--178},
       DOI = {10.1016/S0375-9601(99)00110-3},
       URL = {https://doi.org/10.1016/S0375-9601(99)00110-3},
}

@article {CI01,
    AUTHOR = {Calini, Annalisa and Ivey, Thomas},
     TITLE = {Knot types, {F}loquet spectra, and finite-gap solutions of the
              vortex filament equation},
   JOURNAL = {Math. Comput. Simulation},
  FJOURNAL = {Mathematics and Computers in Simulation},
    VOLUME = {55},
      YEAR = {2001},
    NUMBER = {4--6},
     PAGES = {341--350},
       DOI = {10.1016/S0378-4754(00)00301-3},
       URL = {https://doi.org/10.1016/S0378-4754(00)00301-3},
}

@article {CI21,
    AUTHOR = {Calini, Annalisa and Ivey, Thomas},
     TITLE = {Integrable geometric flows for curves in pseudoconformal
              {$S^3$}},
   JOURNAL = {J.~Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {166},
      YEAR = {2021},
     PAGES = {104249, 17~pages},
       DOI = {10.1016/j.geomphys.2021.104249},
       URL = {https://doi.org/10.1016/j.geomphys.2021.104249},
    EPRINT = {1908.02722},
}

@article {CIM1,
    AUTHOR = {Calini, Annalisa and Ivey, Thomas and Mar\'{\i}-Beffa, Gloria},
     TITLE = {Remarks on {K}d{V}-type flows on star-shaped curves},
   JOURNAL = {Phys.~D},
  FJOURNAL = {Physica~D. Nonlinear Phenomena},
    VOLUME = {238},
      YEAR = {2009},
    NUMBER = {8},
     PAGES = {788--797},
       DOI = {10.1016/j.physd.2009.01.007},
       URL = {https://doi.org/10.1016/j.physd.2009.01.007},
    EPRINT = {0808.3593},
}

@article {CIM2,
    AUTHOR = {Calini, Annalisa and Ivey, Thomas and Mar\'{\i} Beffa, Gloria},
     TITLE = {Integrable flows for starlike curves in centroaffine space},
   JOURNAL = {SIGMA},
  FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and
              Applications},
    VOLUME = {9},
      YEAR = {2013},
     PAGES = {022, 21~pages},
       DOI = {10.3842/SIGMA.2013.022},
       URL = {https://doi.org/10.3842/SIGMA.2013.022},
    EPRINT = {1303.1259},
}

@article {DS,
    AUTHOR = {Doliwa, A. and Santini, P. M.},
     TITLE = {An elementary geometric characterization of the integrable
              motions of a curve},
   JOURNAL = {Phys. Lett.~A},
  FJOURNAL = {Physics Letters~A},
    VOLUME = {185},
      YEAR = {1994},
    NUMBER = {4},
     PAGES = {373--384},
       DOI = {10.1016/0375-9601(94)90170-8},
       URL = {https://doi.org/10.1016/0375-9601(94)90170-8},
}

@incollection {ET1,
    AUTHOR = {Etnyre, John B.},
     TITLE = {Legendrian and transversal knots},
 BOOKTITLE = {Handbook of {K}not {T}heory},
     PAGES = {105--185},
 PUBLISHER = {Elsevier, Amsterdam},
      YEAR = {2005},
       DOI = {10.1016/B978-044451452-3/50004-6},
       URL = {https://doi.org/10.1016/B978-044451452-3/50004-6},
    EPRINT = {math.SG/0306256},
}

@article {EH,
    AUTHOR = {Etnyre, John B. and Honda, Ko},
     TITLE = {Knots and contact geometry~{I}: {T}orus knots and the figure
              eight knot},
   JOURNAL = {J.~Symplectic Geom.},
  FJOURNAL = {The Journal of Symplectic Geometry},
    VOLUME = {1},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {63--120},
       DOI = {10.4310/JSG.2001.v1.n1.a3},
       URL = {https://doi.org/10.4310/JSG.2001.v1.n1.a3},
    EPRINT = {math.GT/0006112},
}

@article {GP1,
    AUTHOR = {Goldstein, Raymond E. and Petrich, Dean M.},
     TITLE = {The {K}orteweg--de {V}ries hierarchy as dynamics of closed
              curves in the plane},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {67},
      YEAR = {1991},
    NUMBER = {23},
     PAGES = {3203--3206},
       DOI = {10.1103/PhysRevLett.67.3203},
       URL = {https://doi.org/10.1103/PhysRevLett.67.3203},
}

@article {GP2,
    AUTHOR = {Goldstein, Raymond E. and Petrich, Dean M.},
     TITLE = {Solitons, {E}uler's equation, and vortex patch dynamics},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {69},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {555--558},
       DOI = {10.1103/PhysRevLett.69.555},
       URL = {https://doi.org/10.1103/PhysRevLett.69.555},
}

@article {HV22,
    AUTHOR = {Haller, Stefan and Vizman, Cornelia},
     TITLE = {A dual pair for the contact group},
   JOURNAL = {Math.~Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {301},
      YEAR = {2022},
    NUMBER = {3},
     PAGES = {2937--2973},
       DOI = {10.1007/s00209-022-03002-x},
       URL = {https://doi.org/10.1007/s00209-022-03002-x},
    EPRINT = {1909.11014},
}

@article {He,
    AUTHOR = {Heller, Lynn},
     TITLE = {Constrained {W}illmore tori and elastic curves in
              2-dimensional space forms},
   JOURNAL = {Comm. Anal. Geom.},
  FJOURNAL = {Communications in Analysis and Geometry},
    VOLUME = {22},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {343--369},
       DOI = {10.4310/CAG.2014.v22.n2.a6},
       URL = {https://doi.org/10.4310/CAG.2014.v22.n2.a6},
    EPRINT = {1303.1445},
}

@article {KW,
    AUTHOR = {Konno, Kimiaki and Wadati, Miki},
     TITLE = {Simple derivation of {B}\"acklund transformation from {R}iccati
              form of inverse method},
   JOURNAL = {Progr. Theoret. Phys.},
  FJOURNAL = {Progress of Theoretical Physics},
    VOLUME = {53},
      YEAR = {1975},
    NUMBER = {6},
     PAGES = {1652--1656},
       DOI = {10.1143/PTP.53.1652},
       URL = {https://doi.org/10.1143/PTP.53.1652},
}

@book {KM97,
    AUTHOR = {Kriegl, Andreas and Michor, Peter W.},
     TITLE = {The convenient setting of global analysis},
    SERIES = {Math. Surveys Monogr.},
    VOLUME = {53},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {1997},
     PAGES = {x+618},
       DOI = {10.1090/surv/053},
       URL = {https://doi.org/10.1090/surv/053},
}

@book {Law,
    AUTHOR = {Lawden, Derek F.},
     TITLE = {Elliptic functions and applications},
    SERIES = {Appl. Math. Sci.},
    VOLUME = {80},
 PUBLISHER = {Springer, New York},
      YEAR = {1989},
     PAGES = {xiv+334},
       DOI = {10.1007/978-1-4757-3980-0},
       URL = {https://doi.org/10.1007/978-1-4757-3980-0},
}

@article {LP,
    AUTHOR = {Langer, Joel and Perline, Ron},
     TITLE = {Curve motion inducing modified {K}orteweg-de {V}ries systems},
   JOURNAL = {Phys. Lett.~A},
  FJOURNAL = {Physics Letters~A},
    VOLUME = {239},
      YEAR = {1998},
    NUMBER = {1--2},
     PAGES = {36--40},
       DOI = {10.1016/S0375-9601(97)00945-6},
       URL = {https://doi.org/10.1016/S0375-9601(97)00945-6},
}

@article {LP91,
    AUTHOR = {Langer, Joel and Perline, Ron},
     TITLE = {Poisson geometry of the filament equation},
   JOURNAL = {J.~Nonlinear Sci.},
  FJOURNAL = {Journal of Nonlinear Science},
    VOLUME = {1},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {71--93},
       DOI = {10.1007/BF01209148},
       URL = {https://doi.org/10.1007/BF01209148},
}

@article {LM19,
    AUTHOR = {Lerario, Antonio and Mondino, Andrea},
     TITLE = {Homotopy properties of horizontal loop spaces and applications
              to closed sub-{R}iemannian geodesics},
   JOURNAL = {Trans. Amer. Math. Soc. Ser.~B},
  FJOURNAL = {Transactions of the American Mathematical Society. Series~B},
    VOLUME = {6},
      YEAR = {2019},
     PAGES = {187--214},
       DOI = {10.1090/btran/33},
       URL = {https://doi.org/10.1090/btran/33},
    EPRINT = {1509.07000},
}

@article {Mi,
    AUTHOR = {Miura, Robert M.},
     TITLE = {Korteweg--de {V}ries equation and generalizations.~{I}. {A}~remarkable explicit nonlinear transformation},
   JOURNAL = {J.~Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {9},
      YEAR = {1968},
     PAGES = {1202--1204},
       DOI = {10.1063/1.1664700},
       URL = {https://doi.org/10.1063/1.1664700},
}

@incollection {M,
    AUTHOR = {Musso, Emilio},
     TITLE = {Liouville integrability of a variational problem for
              {L}egendrian curves in the three-dimensional sphere},
 BOOKTITLE = {Selected {T}opics in {C}auchy--{R}iemann {G}eometry},
    SERIES = {Quad. Mat.},
    VOLUME = {9},
     PAGES = {281--306},
 PUBLISHER = {Seconda Universit\`a di Napoli, Caserta},
      YEAR = {2001},
}

@article {M1,
    AUTHOR = {Musso, Emilio},
     TITLE = {Motions of curves in the projective plane inducing the
              {K}aup--{K}upershmidt hierarchy},
   JOURNAL = {SIGMA},
  FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and
              Applications},
    VOLUME = {8},
      YEAR = {2012},
     PAGES = {030, 20~pages},
       DOI = {10.3842/SIGMA.2012.030},
       URL = {https://doi.org/10.3842/SIGMA.2012.030},
    EPRINT = {1205.5329},
}

@article {MN,
    AUTHOR = {Musso, Emilio and Nicolodi, Lorenzo},
     TITLE = {Hamiltonian flows on null curves},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {23},
      YEAR = {2010},
    NUMBER = {9},
     PAGES = {2117--2129},
       DOI = {10.1088/0951-7715/23/9/005},
       URL = {https://doi.org/10.1088/0951-7715/23/9/005},
    EPRINT = {0911.4467},
}

@article {MNS,
    AUTHOR = {Musso, Emilio and Nicolodi, Lorenzo and Salis, Filippo},
     TITLE = {On the {C}auchy--{R}iemann geometry of transversal curves in
              the 3-sphere},
   JOURNAL = {J.~Math. Phys. Anal. Geom.},
  FJOURNAL = {Journal of Mathematical Physics, Analysis, Geometry},
    VOLUME = {16},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {312--363},
       DOI = {10.15407/mag16.03.312},
       URL = {https://doi.org/10.15407/mag16.03.312},
    EPRINT = {2004.11350},
}

@article {MS,
    AUTHOR = {Musso, Emilio and Salis, Filippo},
     TITLE = {The {C}auchy--{R}iemann strain functional for {L}egendrian
              curves in the 3-sphere},
   JOURNAL = {Ann. Mat. Pura Appl.},
  FJOURNAL = {Annali di Matematica Pura ed Applicata. Series~{IV}},
    VOLUME = {199},
      YEAR = {2020},
    NUMBER = {6},
     PAGES = {2395--2434},
       DOI = {10.1007/s10231-020-00974-7},
       URL = {https://doi.org/10.1007/s10231-020-00974-7},
    EPRINT = {2003.01713},
}

@book {OlverLieGroups,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Applications of {L}ie groups to differential equations},
    SERIES = {Grad. Texts in Math.},
    VOLUME = {107},
 PUBLISHER = {Springer, New York},
      YEAR = {1993},
     PAGES = {xxviii+513},
       DOI = {10.1007/978-1-4612-4350-2},
       URL = {https://doi.org/10.1007/978-1-4612-4350-2},
}

@article {Pi,
    AUTHOR = {Pinkall, Ulrich},
     TITLE = {Hamiltonian flows on the space of star-shaped curves},
   JOURNAL = {Results Math.},
  FJOURNAL = {Results in Mathematics. Resultate der Mathematik},
    VOLUME = {27},
      YEAR = {1995},
    NUMBER = {3--4},
     PAGES = {328--332},
       DOI = {10.1007/BF03322836},
       URL = {https://doi.org/10.1007/BF03322836},
}

@article {V11,
    AUTHOR = {Vizman, Cornelia},
     TITLE = {Induced differential forms on manifolds of functions},
   JOURNAL = {Arch. Math. (Brno)},
  FJOURNAL = {Universitatis Masarykianae Brunensis. Facultas Scientiarum
              Naturalium. Archivum Mathematicum},
    VOLUME = {47},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {201--215},
    EPRINT = {1111.3889},
}

@article {Wa,
    AUTHOR = {Wadati, Miki},
     TITLE = {B\"acklund transformation for solutions of the modified {K}orteweg--de {V}ries equation},
   JOURNAL = {J.~Phys. Soc. Japan},
  FJOURNAL = {Journal of the Physical Society of Japan},
    VOLUME = {36},
      YEAR = {1974},
    NUMBER = {5},
     PAGES = {1498-1498},
       DOI = {10.1143/JPSJ.36.1498},
       URL = {https://doi.org/10.1143/JPSJ.36.1498},
}

@article {W,
    AUTHOR = {Webster, S. M.},
     TITLE = {Pseudo-{H}ermitian structures on a real hypersurface},
   JOURNAL = {J.~Differential Geometry},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {13},
      YEAR = {1978},
    NUMBER = {1},
     PAGES = {25--41},
       DOI = {10.4310/jdg/1214434345},
       URL = {https://doi.org/10.4310/jdg/1214434345},
}
