Integration of the Kaup–Boussinesq system with time-dependent coefficients
We consider the Kaup–Boussinesq system with time-dependent coefficients. We show that the Kaup–Boussinesq system with an additional term is also an important theoretical model, since it is a completely integrable system. We find the time evolution of scattering data for a quadratic pencil of Sturm–L...
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| Veröffentlicht in: | Theoretical and mathematical physics 2023-07, Vol.216 (1), p.961-972 |
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| creator | Babajanov, B. A. Azamatov, A. Sh Atajanova, R. B. |
| description | We consider the Kaup–Boussinesq system with time-dependent coefficients. We show that the Kaup–Boussinesq system with an additional term is also an important theoretical model, since it is a completely integrable system. We find the time evolution of scattering data for a quadratic pencil of Sturm–Liouville operators associated with the solution of the Kaup–Boussinesq system with time-dependent coefficients. The resulting equalities completely determine the scattering data at any
, which allows using the inverse scattering method for solving the Cauchy problem for the Kaup–Boussinesq system with time-dependent coefficients. An example is given to illustrate the application of the obtained results. |
| doi_str_mv | 10.1134/S004057792307005X |
| format | Article |
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| subjects | 14/34 639/766/189 639/766/530 639/766/747 Applications of Mathematics Boussinesq equations Cauchy problems Coefficients Inverse scattering Mathematical and Computational Physics Physics Physics and Astronomy Theoretical Time dependence |
| title | Integration of the Kaup–Boussinesq system with time-dependent coefficients |
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