Darboux Coordinates for the Space of Potentials

  • Sebastian Klein
Part of the Lecture Notes in Mathematics book series (LNM, volume 2229)


In the present chapter we will equip the space of potentials Pot with the structure of an (infinite-dimensional) symplectic manifold, and construct coordinates for this manifold which are adapted to the symplectic structure. By analogy with the finite-dimensional situation, we will call these coordinates Darboux coordinates.


  1. [Da]
    G. Darboux, Sur le problème de Pfaff. Bull. Sci. Math. 6, 14–36, 49–68 (1882)zbMATHGoogle Scholar
  2. [Kapp-P]
    T. Kappeler, J. Pöschel, KdV & KAM, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 45 (Springer, Berlin, 2003)Google Scholar
  3. [Kn-2]
    M. Knopf, Darboux coordinates for periodic solutions of the sinh-Gordon equation. J. Geom. Phys. 110, 60–68 (2016)MathSciNetCrossRefGoogle Scholar
  4. [Pö-T]
    J. Pöschel, E. Trubowitz, Inverse Spectral Theory (Academic Press, London, 1987)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sebastian Klein
    • 1
  1. 1.School of Business Informatics & MathematicsUniversity of MannheimMannheimGermany

Personalised recommendations