Year: 2025
Type: article
Abstract: In this study we derive a rich hierarchy for the Kaup system with timedependent coefficients in the class of rapidly decreasing functions.We show that a hierarchy of the Kaup-Boussinesq system with time-dependent coefficients is also an important theoretical model, since it is a completely integrable system.For solving the problem under consideration, we use the direct and inverse scattering problem of the Sturm-Liouville equation with an energy-dependent potential.The time evolution of the scattering data for the Sturm-Liouville equation with an energy-dependent potential associated with the solution of the hierarchy of the Kaup-Boussinesq system with timedependent coefficients is determined.Using the solution of the inverse scattering problem with respect to the time-dependent scattering data we give an algorithm of constructing the solution of the hierarchy of the Kaup-Boussinesq system with time-dependent coefficients.
Authors: B.A. Babajanov, F.B. Abdikarimov
Institution: Urgench State University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4413028856