ALGORITHM FOR SOLVING THE CAUCHY PROBLEM FOR THE LOADED KORTEWEG-DE VRIES EQUATION WITH AN INTEGRAL TYPE SOURCE IN THE CLASS OF RAPIDLY DECREASING FUNCTIONS
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_41Keywords:
Loaded Korteweg-de Vries equation, Sturm-Liouville operator, Jost solutions, integral equation Gelfand-Levitan-MarchenkoAbstract
The method of the inverse spectral problem is used to integrate the Korteweg-de Vries equation with loaded terms and a self-consistent source of integral type in the class of rapidly decreasing functions. The evolution of the scattering data of the Sturm-Liouville operator is derived, whose coefficient is a solution of the Korteweg-de Vries equation with loaded terms and a self-consistent source of integral type in the class of rapidly decreasing functions.
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