Geodesic
Integrable symplectic maps via reduction of B\"{a}cklund transformation
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 1, pp. 39-50

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We discuss the stationary potential equations as illustrative examples to explain how to construct integrable symplectic maps via Bäcklund transformations. We first give a terse survey of Bäcklund transformations of the potential KdV equation and the potential fifth-order KdV equation. Then, using Jacobi–Ostrogradsky coordinates, we obtain canonical Hamiltonian forms of the stationary potential equations. Finally, we construct symplectic maps from the reduction of a Bäcklund transformation and verify that they are integrable.
Keywords: integrable symplectic map, stationary potential KdV equation, Bäcklund transformation, Lax representation. 
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     title = {Integrable symplectic maps via reduction of {B\"{a}cklund} transformation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Dianlou Du; Yuanyuan Lui; Xue Wang. Integrable symplectic maps via reduction of B\"{a}cklund transformation. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/TMF_2021_208_1_a2/