Integration of the generalized Camassa–Holm equation in the class of periodic functions

We study periodic solutions of the generalized Camassa–Holm equation (CH- $$\gamma$$ equation). We show that the generalized CH- $$\gamma$$ equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH- $$\gamma$$ equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator.

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