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- 2026-yil uchun oliy ta’limdan keyingi ta’lim institutiga ixtisosliklar bo‘yicha Noyabr oyida bo‘lib o‘tadigan qabul imtihonlari savollari
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The dissertation defense was successfully conducted
On February 14, 2026, the dissertation of Ismoilov Oxunjon Bahram ugli for the degree of Doctor of Philosophy (PhD) in the specialty 01.01.02 – “Differential Equations and Mathematical Physics” entitled “Integration of the negative order Korteweg–de Vries and modified Korteweg–de Vries equations using inverse spectral problem methods” was successfully defended.
In this dissertation, the integrability of the Cauchy problem for the negative order KdV equation in the class of rapidly decaying functions was proven using the inverse scattering method for the Sturm–Liouville operator.
Furthermore, the negative order KdV equation with a self-consistent source was solved in the class of rapidly decaying functions using the inverse scattering method for the Sturm–Liouville operator.
The study also proves the integrability of the negative order modified KdV equations with loaded terms and integral sources using the method of solving inverse spectral problems for the Dirac operator in the class of periodic functions.
The obtained results are significant for the development of the theory of differential equations and mathematical physics.