Following the announcement of the results of the first call of the TÜBİTAK-1001 Program for the year 2025 in August 2025, a new project led by Assoc. Prof. Dr. Cihangir Özemir from the Mathematics Department has been selected for funding. The funded project is entitled “Algebraic Properties and Solutions in Evolution Equations of Wave Packets”.

The research team, led by Assoc. Prof. Dr. Özemir, brings together experts and researchers from multiple institutions. The team includes postdoctoral researcher Dr. Ayşe Tiryakioğlu and Ph.D. students Res. Assist. Şeyma Gönül, Yasemin Çalış (Kabataş Erkek High School), and Yasin Hasanoğlu. Additionally, the project features collaborative efforts from Assoc. Prof. Dr. Mehmet Fatih Uçar of Istanbul Kültür University and Assoc. Prof. Dr. Gülden Gün Polat of Gebze Technical University.

The primary aim of this project is to investigate two different systems in the family of Davey-Stewartson equations using Lie group analysis of differential equations and to search for analytical and numerical solutions. The wave models under consideration were first formulated in 2 space and 1 time dimension as a set of nonlinear partial differential equations modeling the time evolution of the long and short wavelength vibrational components of a wave packet propagating in shallow water. Since its first introduction to the literature, this framework has been the subject of research in many fields, such as fluid mechanics, mathematical physics, integrable systems, numerical analysis, and the qualitative analysis of partial differential equations. In today's literature, these models also appear in the modeling of electron-acoustic waves in plasma physics and are the subject of numerical solution and simulation-supported research.

Ultimately, the project aims at enlightening the algebraic and analytical properties of these complicated models and bringing new insights to the available literature, thereby providing a strong foundation for future developments in the field.