Abstract
In the present chapter we will equip the space of potentials P o t 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.
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References
G. Darboux, Sur le problème de Pfaff. Bull. Sci. Math. 6, 14–36, 49–68 (1882)
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)
M. Knopf, Darboux coordinates for periodic solutions of the sinh-Gordon equation. J. Geom. Phys. 110, 60–68 (2016)
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Klein, S. (2018). Darboux Coordinates for the Space of Potentials. In: A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation. Lecture Notes in Mathematics, vol 2229. Springer, Cham. https://doi.org/10.1007/978-3-030-01276-2_14
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DOI: https://doi.org/10.1007/978-3-030-01276-2_14
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