Abstract
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.
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This work was supported by National Natural Science Foundation of China (Project No. 11271337).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 208, pp. 39-50 https://doi.org/10.4213/tmf10023.
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Du, D., Liu, Y. & Wang, X. Integrable symplectic maps via reduction of Bäcklund transformation. Theor Math Phys 208, 886–895 (2021). https://doi.org/10.1134/S0040577921070035
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DOI: https://doi.org/10.1134/S0040577921070035