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Academic Seminar-Training Held at UrSU with Dr. Gayrat Urazbaev

An academic seminar-training was held at the Faculty of Physics and Mathematics of Urgench State University, featuring Dr. Gayrat Urazalievich Urazbaev, a Leading Researcher at the Khorezm Branch of the V.I. Romanovskiy Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan.

During the seminar, Dr. Gayrat Urazbaev delivered a lecture and presentation titled: "Integration of nonlinear evolutionary equations with self-consistent sources using the inverse scattering transform method".

Core Scientific Topics Covered During the Seminar-Training:

The speaker elaborated on the theoretical foundations of integrating nonlinear evolutionary equations using the Inverse Scattering Transform Method (ISTM) and provided an in-depth analysis of the following current research fields:

  • Direct and Inverse Problems: The formulation of direct and inverse problems for the Sturm-Liouville operator and the Dirac system.
  • Potential Reconstruction: Methods of reconstructing the potential via the Gelfand–Levitan–Marchenko integrals and equations.
  • Practical Application: A detailed demonstration of the integration process of the loaded nonlinear Schrödinger equation of negative order using the inverse scattering method for the Dirac operator.

Recommendations for International Publications: Beyond theoretical topics, the seminar provided valuable advice for young scientists and researchers on how to successfully publish their significant research findings in prestigious international journals indexed in Scopus and Web of Science databases.

 Dynamic Q&A and Discussions

At the end of the seminar-training, participating faculty members, young researchers, and master's students actively engaged with questions on the subject matter. In particular, a lively exchange of ideas took place regarding:

1.Future prospects of applying the inverse scattering transform method in modern scientific research;

2.The regularity (smoothness) of solutions to the Gelfand–Levitan–Marchenko equations;

3.The specific characteristics of nonlinear equations of negative order.

The seminar was conducted at a high academic level and will serve as a vital cornerstone for the department's researchers.

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