On the Integration of the Periodic Camassa–Holm Equation with an Integral-Type Source
Bazar BabajanovUrgench State University and Khorezm Branch of Academy of Sciences of Sciences of Uzbekistan, Romanovskiy Institute of Mathematics, 220100, Urgench, UzbekistanDilshod AtajonovUrgench State University and Khorezm Branch of Academy of Sciences of Sciences of Uzbekistan, Romanovskiy Institute of Mathematics, 220100, Urgench, Uzbekistan
ABI
Аннотация
In the present paper, we study the integration of the periodic Camassa–Holm equation with an integral-type source. Physically, sources arise in solitary waves with a variable speed and lead to a variety of dynamics of physical models. With regard to their applications, these kinds of systems are usually used to describe interactions between different solitary waves. We show that the periodic Camassa–Holm equation with an integral-type source is also an important theoretical model as it is a completely integrable system. We obtain a representation for the solution of periodic Camassa–Holm equation with an integral-type source in the framework of the inverse spectral problem for a weighted Shturm–Liouville operator.
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