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The dissertation defense was successfully conducted

On November 22, 2025, the dissertation of Sobirov Shexzod Quchqarboy ugli for the degree of Doctor of Philosophy (PhD) in the specialty 01.01.02 – “Differential Equations and Mathematical Physics” entitled “Integration of the loaded modified Korteweg–de Vries equation with a self-consistent source in the class of rapidly decaying functions” was successfully defended.

In this dissertation, the integrability of modified KdV equations with additional terms and self-consistent sources with time-dependent coefficients was proven in the class of rapidly decaying functions under the condition that the non-self-adjoint Dirac operator has simple eigenvalues.

The solvability of the Cauchy problem for these equations was established in the same class of functions. Cases where the Dirac operator has multiple eigenvalues were also investigated, and the integrability of the corresponding equations as well as solutions to the Cauchy problems were obtained.

Furthermore, solutions were constructed for integral-type equations with self-consistent sources in the class of rapidly decaying functions.

The inverse scattering method was applied to integrate the loaded modified KdV equation with a self-consistent source.

The obtained results are significant for the development of differential equations and mathematical physics.

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