基于逆散射法的自洽源kap - boussinesq系统集成

Pub Date : 2022-06-01 DOI:10.35634/vm220201

B. B.A., Azamatov A.Sh.

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引用次数: 0

摘要

在本研究中，我们考虑具有自洽源的kap - boussinesq系统。我们证明了具有自洽源的kap - boussinesq系统可以用逆散射理论的方法进行积分。为了解决所考虑的问题，我们使用了具有能量依赖势的Sturm-Liouville方程的正反散射问题。确定了具有自洽源的kap - boussinesq系统解与能量依赖势相关联的Sturm-Liouville方程散射数据的时间演化。所得到的等式完全确定了任意$t$的散射数据，使得应用逆散射问题的方法求解具有自洽源的kap - boussinesq系统的Cauchy问题成为可能。

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Integration of the Kaup–Boussinesq system with a self-consistent source via inverse scattering method

In this study we consider the Kaup–Boussinesq system with a self-consistent source. We show that the Kaup–Boussinesq system with a self-consistent source can be integrated by the method of inverse scattering theory. For a 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 potentials associated with the solution of the Kaup–Boussinesq system with a self-consistent source is determined. The obtained equalities completely determine the scattering data for any $t$, which makes it possible to apply the method of the inverse scattering problem to solve the Cauchy problem for the Kaup–Boussinesq system with a self-consistent source.

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