Abstract
Integrable systems constitute an essential part of modern physics. Traditionally, to approve a model is integrable one has to find its infinitely many symmetries or conserved quantities. In this letter, taking the well known Korteweg-de Vries and Boussinesq equations as examples, we show that it is enough to find only one nonlocal key-symmetry to guarantee the integrability. Starting from the nonlocal key-symmetry, recursion operator(s) and then infinitely many symmetries and Lax pairs can be successfully found.
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Acknowledgments
The authors are in debt to the helpful discussions with Professors X. B. Hu and Q. P. Liu. The authors acknowledge the support of the National Natural Science Foundation of China (Nos. 12275144, 12235007 and 11975131) and K. C. Wong Magna Fund in Ningbo University.
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Lou, S.Y., Jia, M. From one to infinity: symmetries of integrable systems. J. High Energ. Phys. 2024, 172 (2024). https://doi.org/10.1007/JHEP02(2024)172
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DOI: https://doi.org/10.1007/JHEP02(2024)172