I am Dr. Ananya Tripathy, a mathematician specializing in the analytical investigation of nonlinear partial differential equations (PDEs) and their applications in mathematical physics. My research focuses on deriving exact and solitary-wave solutions to nonlinear mathematical models, with particular emphasis on understanding the interplay between nonlinearity, dispersion, phase modulation, and wave stability. My work spans nonlinear optics, optical solitons, fractional-order differential equations, spin dynamics, shallow-water waves, and elastic media. I employ a combination of analytical techniques, symbolic computation, and graphical visualization to explore wave propagation, stability, and the physical significance of mathematical solutions. My broader research interests include mathematical modelling, pattern formation, phase transitions, data analysis, and emerging machine-learning approaches, particularly physics-informed neural networks (PINNs).

My teaching interests encompass both fundamental and applied mathematics, including ordinary and partial differential equations, complex analysis, probability theory, applied statistics, and mathematical modelling. I strive to create an engaging, student-centered learning environment that connects mathematical theory with computational methods, visual intuition, and practical applications. Through my teaching and mentoring experience, I aim to develop students’ analytical reasoning, problem-solving abilities, and independent thinking. I am particularly interested in fostering interdisciplinary learning and encouraging students to explore how mathematical tools can address complex problems in engineering, physics, and the applied sciences.