New discovery may revolutionize decades-old understanding of integrable hierarchies

Processes in nature can often be described by equations. In many non-trivial cases, it is impossible to find the exact solutions to these equations. However, some equations are much simpler to deal with because of their extreme symmetries. An important class of such equations is given by integrable systems. Integrable systems are known to be a universal tool in theoretical physics and mathematics. They have proven to be extremely useful in diverse areas such as statistical mechanics, gauge theories, quantum gravity, and nonlinear waves, and they are particularly important in modern geometry.

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