Principal Investigator of the project Jambul Yusupov has visited the University of Wuppertal (Germany) from July 17 to August 08 to discuss with a foreign Co-PI of the project prof. Matthias Ehrhardt the project implementation plan, detailed work, as well as to agree a travel schedule from both sides. In addition, the relevance, formulation, and ways of solving the tasks were discussed.
Project Investigator J. Yusupov and foreign Co-PI prof. M. Ehrhardt during discussions (Institute of Mathematical Modelling, Analysis and Computational Mathematics).
During the secondment, a visit was also made to the University of Ilmenau (Germany) for the purpose of cooperation on the subject of the project. Problems for joint solution and preparation of articles for publication of the results were discussed.
Talk of the project investigator, J. Yusupov, at the seminar of professor C. Trunk’s group “Applied Functional Analysis” (Institute of Mathematics, Ilmenau)
As part of the project management plan, professor D.U. Matrasulov visited the University of Wuppertal (Germany) from December 13, 2022 to December 17, 2023, where he and the foreign Co-PI of the project discussed the formulation of tasks, considered in the project plan to be solved for the next year.
The research results were also presented at the international conference “Dynamics Days Central Asia & Caucasus” (23.09.2023-30.09.2022) and the summer school “Modern trends in quantum science & technologies: From quantum materials to quantum information” (22.09.2023-02.10 .2023), held at Baku State University (Azerbaijan).
During the period of this secondment to the foreign Co-PI’s university, the annual report on scientific research done in the collaboration, the tasks to be solved together with the partner, and the planned work were discussed. Problem solving approaches were adjusted considering new research results published during the reporting period.
Talk of the project investigator, J. Yusupov at the seminar of professor M. Ehrhardt’s group. (University of Wuppertal, Germany)
During the secondment, a visit was also made to the Institute of Nuclear Physics of the Czech Academy of Sciences and the Czech Technical University in Prague for the purpose of cooperation on the subject of the project. Problems for joint solution and preparation of articles for publication of the results were discussed.
Project investigator J. Yusupov and professor P. Exner during discussions (Institute of Nuclear Physics of the Czech Academy of Sciences, Řež, Prague)
Talk of the project investigator, J. Yusupov, at the seminar of professor P. Exner’s group. (Czech Technical University, Prague, Czech Republic)
In August professor D.U. Matrasulov visited the University of Wuppertal (Germany), where he and the foreign Co-PI of the project discussed the formulation of tasks, considered in the project plan to be solved for the next year.
The research results were also presented at the international conference “Mathematics for the Micro/Nano-World: From soliton dynamics, nonlinear optics to quantum science and technology” (September 18-22, 2023), held at Samarkand State University (Uzbekistan).
During the secondment to the university of the foreign Co-PI, discussions were held regarding the annual report on joint scientific research. Current results, upcoming tasks, and the planned work for the forthcoming period were reviewed.
As part of the visit, approaches to solving research tasks were adjusted, taking into account recent publications and studies released during the reporting period. These adjustments made it possible to adapt research methods to more effectively achieve the set goals and identify potential directions for further scientific collaboration.
Project Investigator J. Yusupov and foreign Co-PI prof. M. Ehrhardt during discussions (Institute of Mathematical Modelling, Analysis and Computational Mathematics, Wuppertal).
The research results were also presented at the international conference and summer school “International Summer School & Conference on Evolution Equations, Approximation and Spectral Optimization” (Almaty, Kazakhstan, September 16–18, 2024) and at “Dynamics Days Central Asia and Caucasus: 21st Century Silk Road for Science and Peace” (Samarkand, Uzbekistan, October 1–5, 2024).
Professor Carsten Trunk visited KIUT to discuss current project challenges, address prospective issues, and explore opportunities for further collaboration.
In the current year of project implementation, the secondment to the university of the foreign Co-PI (Bergische Universität Wuppertal) was complemented by visits to the Institute of Nuclear Physics of the Czech Academy of Sciences and to the Ilmenau University of Technology (Germany). These visits included in-depth discussions on the annual report concerning joint scientific research. The current results, forthcoming tasks, and the planned work for the next reporting period were reviewed.
As part of these interactions, approaches to addressing the research objectives were refined, taking into account recent publications and studies released during the reporting period. Ongoing projects were discussed alongside newly formulated ones, including the study of transparent boundary conditions (TBC) for periodic structures, the position-dependent mass Schrödinger equation in branched structures, TBC for Bogoliubov–de Gennes (BdG) and Dirac equations and TBC for partial differential equations in complex structures via Titchmarsh–Weyl theory.
During the secondment, a visit was also made to the Institute of Nuclear Physics of the Czech Academy of Sciences to explore and strengthen collaboration related to the project’s research objectives.
Another visit was also carried out to Ilmenau Technical University to enhance research collaboration and promote the exchange of knowledge and expertise within the framework of the project.
Professor Carsten Trunk from Ilmenau Technical University visited KIUT in September to discuss joint research topics and strengthen collaboration within the framework of the project.
During the final year of the project, the project team continued its international research collaboration through scientific secondments to partner institutions in Germany.
From 2 July to 15 July 2026, the Principal Investigator visited Ilmenau University, where intensive research was carried out in collaboration with Prof. Carsten Trunk, Prof. Henrik Winkler, and Valeriy Heinz. The visit focused on ongoing joint research activities and the development of new research directions.
Following the visit to Ilmenau, the Principal Investigator visited the University of Wuppertal (from 16 July to 20 July 2026), where research meetings were held with the project Co-Principal Investigator, Prof. Matthias Ehrhardt. In addition, another project member, Dr. Jasurbek Matrasulov, also visited the University of Wuppertal as part of his research stay, which was combined with his DAAD-funded project.
These visits provided an excellent opportunity to review the progress of the project, advance ongoing research, and explore new directions for future international collaborations and joint funding proposals. The discussions covered a broad range of current research topics, including transparent boundary conditions (TBCs) for the heat equation on metric graphs, the Fokker–Planck equation, the stationary Schrödinger equation on branching domains using Weyl–Titchmarsh theory, the Dirac equation, and the Bogoliubov–de Gennes (BdG) equation, extending the work initiated during the previous year. Significant attention was also devoted to the development of transparent boundary conditions for the stationary Schrödinger equation with position-dependent mass via Weyl–Titchmarsh theory, along with several other collaborative research directions in mathematical physics and numerical analysis.
In addition to the planned scientific secondments, D. Matrasulov and J. Yusupov participated as invited speakers in the international conference Dynamics Days Central Asia and Caucasus, held in Astana, Kazakhstan, on 25–28 May 2026. During the conference, they presented research results obtained within the framework of the project, thereby disseminating the project outcomes to the international scientific community and strengthening academic collaboration with researchers in the field.
As this was the final year of the project, particular attention was devoted to evaluating the outcomes of the collaboration and planning future joint research initiatives. The project team confirms that the scientific objectives and planned research goals of the project have been successfully achieved.