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The dissertation defense was successfully conducted
On February 14, 2026, the dissertation of Atanazarova Shoira Erkinovna for the degree of Doctor of Philosophy (PhD) in the specialty 01.01.02 – “Differential Equations and Mathematical Physics” entitled “Integration of the modified Korteweg–de Vries equation of negative order with a self-consistent source” was successfully defended.
In this research, evolution equations were derived using the inverse scattering method based on the scattering data of the Zakharov–Shabat system with rapidly decaying potentials associated with the negative order mKdF equation. It was proven that the constructed potential represents the solution of the Cauchy problem in the class of rapidly decaying functions.
The study also established the complete integrability of the considered equation and constructed multi-soliton solutions using the triple matrix method. Integration problems were solved for the case of moving eigenvalues.
Furthermore, the matrix form of the negative order mKdF equation was integrated using the inverse scattering method for the corresponding matrix Zakharov–Shabat system, and solutions to the Cauchy problem were obtained in the class of rapidly decaying functions.
The results of the dissertation contribute significantly to modern mathematical physics and the theory of differential equations.