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

B. A. Babajanov, D. O. Atajonov

Urgench State University named after Al-Khorezmi, Urgench, Uzbekistan

Abstract: 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.

Keywords: CH-$\gamma$ equation, generalized Camassa–Holm equation, trace formulas, inverse spectral problem, weighted Sturm–Liouville operator.

Received: 16.01.2025
Revised: 09.02.2025

DOI: 10.4213/tmf10890

 English version: Theoretical and Mathematical Physics, 2025, 223:1, 624–635

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