Home address: Home № 47b, flat 2, Str. R. Gaipov, city of Urgench,
region of Khorezm, UZBEKISTAN.
Postal Code: 220102
Phone (mob, home): +998972119910, +998622256789
E-mail: iroda-b@
Date of birth: 06.10.1980
EDUCATION
1997-2001 BA student of the Mathematics faculty of Urgench State
University
2001-2003 MA student of the mathematics faculty, on specialty “Differential
Equations”, of Urgench State University
2008-2012 PhD student of the Physics-Mathematics faculty of Urgench
State
University.
5 July 2012 defended PhD work on specialty “Mathematical Physics” at the
National University of Uzbekistan in Tashkent.
2022-present Postdoctoral researcher
RESEARCH, TEACHING, or OTHER INTERESTS
, Mathematics, Mathematical Physics, Analysis
FUTURE PROJECTS
Integration nonlinear evolution equations via inverse and direct methods.
Applications Invited
19
Scopus Publications
Scopus Publications
Integration of the negative order Nonlinear Schrödinger Equation with self-consistent source G.U. Urazboev, I.I. Baltaeva Bulletin of the Karaganda University Mathematics Series, 2026 This paper focuses on the integrability properties of the negative-order nonlinear Schro¨dinger equation with a source. The source consists of the combination of the eigenfunctions of the corresponding spectral problem for the Dirac system which has not spectral singularities. The connection between the negative-order nonlinear Schro¨dinger equation with a self-consistent source and the Dirac system of equations is crucial, as it allows the complex dynamics of the original nonlinear model to be interpreted through the spectral theory of the Dirac operator. Building on this relationship, the evolution equations for the scattering data of the Dirac operator are derived, which is the central part in the inverse scattering transform (IST) framework. Due to the IST procedure, the rapidly decaying potential of the Dirac operator can be reconstructed from the derived differential equations for the scattering data, and this potential corresponds precisely to the solution of the problem under consideration. To illustrate the practical value of the theoretical results, the paper presents a detailed example demonstrating each stage of the method, from the formulation of the scattering data to the final reconstruction of the potential. This example clarifies the overall procedure and highlights the effectiveness of the approach in concrete applications.
Exploring solutions for the negative-order modified Korteweg–de Vries equation with a self-consistent source corresponding to moving eigenvalues G. U. Urazboev, I. I. Baltaeva, Sh. E. Atanazarova Theoretical and Mathematical Physics Russian Federation, 2025 Abstract We focus on investigating the negative-order modified Korteweg–de Vries equation with a special source. Based on the inverse scattering transform method, we derive the temporal dependency of scattering data for the Dirac operator with moving eigenvalues. We derive the multisoliton solution to considered problem using matrix triplet method and illustrate the wave behavior of solutions in both presence and absence of a source.
Analysis of the solitary wave solutions of the negative order modified Korteweg –de Vries equation with a self-consistent source G.U. Urazboev, I.I. Baltaeva, Sh.E. Atanazarova Partial Differential Equations in Applied Mathematics, 2025 In this work, the initial value problem for the negative order modified Korteweg–de Vries equation (nmKdV) with a self-consistent source was analyzed. The inverse scattering transform method for obtaining evolution equations of scattering data of the Dirac operator, which potential is the solution of the considered problem was implemented. For the first time, the real matrix triplet ( A , B , C ) method was applied to construct a multisoliton solution of nmKdV equation with a self-consistent source. Furthermore, the wave phenomena of solitons were demonstrated by varying the normalization conditions. • The considered operator has no spectral singularities and all eigenvalues are simple. • The Jost functions admit an analytical continuation to the upper-half plane. • The potential is reconstructed through the scattering data of the Dirac system. • The soliton solution arise in the case of reflectionless coefficient.
SOLVING THE NEGATIVE ORDER KORTEWEG-DE VRIES EQUATION WITH A SELF-CONSISTENT SOURCE CORRESPONDING TO MOVING EIGENVALUES G. Urazboev, I. Baltaeva International Journal of Applied Mathematics, 2025 This study focuses on addressing the negative order Korteweg-de Vries (KdV) equation with a self-consistent source associated with dynamic eigenvalues, using the inverse scattering transform (IST).The primary goal is to establish the evolution of the scattering data for the spectral problem linked to the negative-order Korteweg-de Vries equation with a self-consistent source and moving eigenvalues.The derived relationships fully describe the evolution of the scattering data, enabling the application of the IST technique to solve the given problem.
INTEGRATION OF LOADED NONLINEAR SCHRÖDINGER EQUATION IN CLASS OF FAST DECAYING FUNCTIONS Gayrat Urazalievich Urazboev, Iroda Ismailovna Baltaeva, Ilkham Davronbekovich Rakhimov Ufa Mathematical Journal, 2025 We show that the inverse scattering transform technique can be applied to obtain the time dependence of scattering data of the Zakharov - Shabat system, which is described by the loaded nonlinear Schrödinger equation in the class of fast decaying functions. In addition we prove that the Cauchy problem for the loaded nonlinear Schrödinger equation is uniquely solvable in the class of rapidly decreasing functions. We provide the explicit expression of a single soliton solution for the loaded nonlinear Schrödinger equation. As an example, we find the soliton solution of the considered problem for an arbitrary non - zero continuous function $\gamma(t).$
Deep Learning-Based Real-Time Interfaces for Monitoring and Predictive Control of Intensive Care Unit Patient Parameters Kiran Kumar, Suneet Gupta, Kapil Shrivastava, Iroda Baltaeva, Nidal Al Said, Faheem Ahmad Reegu 2025 IEEE 5th International Conference on ICT in Business Industry and Government Ictbig 2025, 2025 The end goal of this work is to develop a complete system that uses deep learning to keep an eye on and predict data in real time for patients in intensive care units. With the assistance provided by this project, monitoring patients on time can become more accurate and consistent. After giving the networks their anticipated parameters and risk ratings, their performance is enhanced by using a number of methods, such as residual weighting, temporal smoothing, and multi-objective optimization, to name a few. This happens right after the networks finish the prediction operation. Medical personnel should be able to make better judgments by using predictive control methods such as proportional-derivative adjustments, trend analysis, and anomaly detection. If we use these methods, we can fix the problems and turn on the alerts. After all the processing and modeling were done, it looks like the prediction's dependability, the reduction's accuracy, the warning's timeliness, the signal quality, and the calculation's efficiency have all gone up a lot. The recommended method could provide better care for patients in the critical care unit. It ensures that trajectories align with the body's functions, alarms trigger quickly, and real-time data analysis occurs swiftly. These results suggest that the paradigm might make critical care organizations perform better, help uncover problems sooner, and make patients safer. We may then utilize this paradigm to develop sophisticated, data-driven systems for monitoring patients in intensive care units.
Deep Learning-Based Multimodal Fusion Techniques for Enhanced Diagnosis and Prognosis in Complex Medical Imaging Scenarios Mihir Harishbhai Rajyaguru, Aishwarya Selvam, Shubha Vakulabharanam, Mukesh Soni, Faheem Ahmad Reegu, Iroda Baltaeva 2025 IEEE 5th International Conference on ICT in Business Industry and Government Ictbig 2025, 2025 The primary objective of this project is to enhance the diagnostic and prognostic capabilities of medical imaging modalities through the development of a Deep Learning-Based Multimodal Fusion Framework (DMFF). The suggested paradigm ensures data integrity while reducing the effects of perceptual biases. Residual and latent projection layers use spatial, temporal, and cross-modal attention processes to achieve this. Attention-guided aggregation, temporal modeling, and convolutional feature encoding let the system swiftly sync up many different sorts of images. Positron emission tomography (PET), computed tomography (CT), and magnetic resonance imaging (MRI) are some of these imaging methods. When compared to more advanced baselines like FTTransformer and TabPFN, the model's false positive rate of 4.9% is fine. It had a false positive rate of 92.5%, an area under the curve of 97.3%, and an area under the probability curve of 96.2% when evaluated on many benchmark datasets. These results are quite excellent. It is clear that all of these wonderful results are there following the test. If we use robustness tests that look at changes in the domain and other factors, we might acquire further proof that the system can generalize. The test results reveal that performance has dropped a bit since the area under the curve (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta \text{AUC}$</tex>) is less than 1.8%. The findings of the analysis reveal that the DMFF framework is straightforward to grasp, consistent, and works well for calculations. It is also being evaluated for usage in therapeutic settings, which is an intriguing new finding.
Soliton solutions of the negative-order nonlinear Schrödinger equation G. U. Urazboev, I. I. Baltaeva, A. K. Babadjanova Theoretical and Mathematical Physics Russian Federation, 2024 We discuss the integration of the Cauchy problem for the negative-order nonlinear Schrödinger equation in the class of rapidly decreasing functions via the inverse scattering problem method. In particular, we obtain the time dependence of scattering data of the Zakharov–Shabat system with the potential that is a solution of the considered problem. We give an explicit representation of the one-soliton solution of the negative-order nonlinear Schrödinger equation based on the obtained results.
Integration of the Loaded Sine-Gordon Equation by the Inverse Scattering Problem Method G.U. Urazboev, I.I. Baltaeva, A.T. Baimankulov Azerbaijan Journal of Mathematics, 2024 In this paper, we consider the Cauchy-Goursat problem for a loaded sine-Gordon equation.The main results of the work are the theorem on the uniqueness of the solution of the problem under consideration and the theorem on the evolution of the scattering data of the Dirac operator whose potential is related to the solution of the loaded sine-Gordon equation.The equalities obtained in the scattering data evolution theorem make it possible to apply the method of inverse scattering problem to solve the considered problem.
Soliton Solutions of the Negative Order Modified Korteweg – de Vries Equation Urgench State University, G. U. Urazboev, I. I. Baltaeva, Urgench State University, Sh. E. Atanazarova, Urgench State University, Khorezm branch of V. I. Romanovski Institute of Mathematics, Uzbekistan Academy of Science Bulletin of Irkutsk State University Series Mathematics, 2024
