From one to infinity: symmetries of integrable systems
Author:
S. Y. Lou, M. Jia
Keyword:
Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)
journal:
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date:
2023-09-12 16:00:00
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.