Integration of the mKdV Equation with nonstationary coefficients and additional terms in the case of moving eigenvalues

A. B. Khasanov, U. Hoitmetov, Sh.Q. Sobirov
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Abstract

In this paper, we consider the Cauchy problem for the non-stationary modified Korteweg–de Vries equation with an additional term and a self-consistent source in the case of moving eigenvalues. Also, the evolution of the scattering data of the Dirac operator is obtained, the potential of which is the solution of the loaded modified Korteweg–de Vries equation with a self-consistent source in the class of rapidly decreasing functions. Specific examples are given to illustrate the application of the obtained results.
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带有非平稳系数和附加项的mKdV方程在移动特征值情况下的积分
本文研究了带有附加项和自洽源的非平稳修正Korteweg-de Vries方程在移动特征值情况下的Cauchy问题。同时,得到了Dirac算子散射数据的演化过程,其势为速降函数类中具有自相容源的加载修正Korteweg-de Vries方程的解。通过具体实例说明所得结果的应用。
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