From one to infinity: symmetries of integrable systems

S. Y. Lou; M. Jia

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arXiv · 2309.06729

From one to infinity: symmetries of integrable systems

S. Y. Lou·M. Jia

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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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S. Y. Lou, M. Jia. 2023-09-13. From one to infinity: symmetries of integrable systems. https://arxiv.org/abs/2309.06729

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