Nonlinear partial differential equations, mathematical modeling, solitons, symmetry methods, and their applications in physics, optics, and epidemic models.

Dr. Lakhveer Kaur is an Associate Professor in the Department of Mathematics at Jaypee Institute of Information Technology (JIIT), Noida, with over fifteen years of teaching and research experience in applied and mathematical sciences. Her research expertise lies in nonlinear partial differential equations, mathematical modeling, soliton theory, optics, and symmetry methods. She has made a significant and original contribution to the field through the discovery and introduction of the Wazwaz–Kaur Boussinesq (WKB) equation, a generalized multidimensional nonlinear wave model that has enriched the theoretical framework of nonlinear wave propagation and admits a wide range of exact analytical solutions. Dr. Kaur has an outstanding research profile with an extensive list of publications in reputed international journals indexed in SCIE and Scopus. She has been recognized among the World’s Top 2% Scientists by Elsevier and Stanford University for four consecutive years (2021–2024) and is ranked among the top 0.5% scholars worldwide by ScholarGPS (2024). She has also been selected as an ICMS Visiting Fellow 2024 at Edinburgh, UK, and is a recipient of the Distinguished Women Scientist Award (India Research Tour 2025) by Springer Nature and ICSSR. Her academic excellence is further reflected through awards such as the Most Cited Article Award from IOP and the Trusted Reviewer Status from the Institute of Physics. In addition to her research contributions, Dr. Kaur has successfully supervised Ph.D. scholars, led funded research projects supported by the National Board for Higher Mathematics (NBHM), and served as an external examiner for postgraduate and doctoral theses in India and abroad. She has authored and edited books published by Springer, Nova Science Publishers, and Lambert Academic Publishing. Actively involved in academic leadership, she has organized international conferences, faculty development programs, and workshops, and has delivered numerous invited and expert lectures at national and international forums. Through her teaching, research, and academic service, Dr. Lakhveer Kaur continues to make impactful contributions to mathematics and interdisciplinary scientific research. Reference: Exploitation of Symmetry Based Invariant Solutions for Nonlinear Partial Differential Equations   Symmetry plays a fundamental role in the analysis and solution of nonlinear partial differential equations (PDEs), providing a systematic mechanism for reducing complexity and uncovering exact solution structures. This session presents the exploitation of Lie group symmetries to derive invariant solutions of nonlinear PDEs through symmetry reductions to lower-dimensional PDEs and ordinary differential equations. Emphasis is placed on the construction of Lie symmetry algebras, invariant surface conditions, and similarity variables that lead to group-invariant solutions. Representative examples illustrate how symmetry-based methods generate physically relevant structures such as solitons, different types of waves, periodic solutions and how they are presented graphical to capture important characteristics of concerned physical phenomenon. The talk highlights symmetry as a unifying and rigorous tool for revealing hidden geometric structures and for advancing the analytical understanding of nonlinear PDEs in higher dimensions.