Nonlinear Partial Differential Equations

This book presents select proceedings of the 4th International Conference on Applied Mathematics in Science and Engineering (AMSE-2025). It addresses the latest research and advancements in Nonlinear Dynamics and Partial Differential Equations (PDEs) in Applied Mathematics. Nonlinear dynamics play a crucial role in understanding and solving complex natural and technological phenomena, with its applications in PDEs remaining a rapidly evolving field. Featuring contributions from leading experts, this book provides an in-depth exploration of nonlinear dynamical systems, emphasizing their applications in analyzing, modeling, and solving PDEs across different disciplines. Covering a broad spectrum of topics, the book delves into theoretical foundations, numerical techniques, and real-world applications. Key themes include multi-faceted applications of fundamental laws & analytical/numerical methods of applied mathematics. Designed for researchers, advanced students, and professionals, this book provides a comprehensive resource by bridging theory and application, inspires further investigation, promotes interdisciplinary collaboration, and makes substantial contributions to the advancement of knowledge.

Apul Narayan Dev is currently working as Professor, Department of Mathematics, Siksha O Anusandhan Deemed to be University, Bhubaneswar. He did his M. Sc., M.Phil, and Ph.D. in Mathmatics from Gauhati University in 2009, 2011 and 2016, respectively. His areas of interest are Basic Study of theoretical Plasmas, Degenerate Mathematical method, & Fluid dynamics. He has published nearly 48 papers in international SCI/Scopus indexed journals and one book entitled “Shock wave Phenomena in Dusty Plasma”. He has guided 1 research scholar and four more students are working under his supervision for their PhD. He has organized three International Conferences (AMSE-2019, AMSE-2022, and AMSE-2024), two International webinars (Maple-2020 and Mathematica-2020), and one workshop (MAMLPSP-2024). He has also edited a SCOPUS indexed Conference Proceeding with AIP Publisher in 2022 as a leading Editor. He is also the editor of the book ‘Design Optimization Using Artificial Intelligence’ under CRC Publishers, and is currently working as a Guest Editor for a special issue in ‘Journal of Interdisciplinary Mathematics’.

Sayantan Guha obtained his Ph.D. degree from the Department of Mathematics and Computing at IIT(ISM), Dhanbad, India, on 2022 and currently works as an Assistant Professor at the Centre for Data Science, Institute of Technical Education & Research (ITER), Siksha ‘O’ Anusandhan University, Odisha, India. His research work covers broad areas involving micromechanical modeling of smart composites, investigating wave reflection/transmission phenomenon, studying surface wave propagation, and analyzing thermoelastic damping & frequency of different types of micro/nano-scale beams with complexities. He has published more than 25 SCI/SCIE international journal articles & 3 book chapters to date. He has participated in several academic conferences and gave speeches and invited talks. He also received prestigious scholarships, awards, and honors like the “Young Scientist Award” at 65th ISTAM (2020), etc. Currently, one student is working under his supervision for his PhD degree.

Jalil Manafian, Ph.D., is Professor in the Department of Applied Mathematics, Faculty of Mathematical Science, University of Tabriz. Professor Manafian works in the field of Applied Mathematics and numerical analysis. His main research lies in studying nonlinear partial differential equations, solitons, optical solitons, Hirota bilinear method, Lie symmetric method, numerical and analytical methods.    Dr. Manafian studied Applied Mathematics in Amirkabir University of Technology and University of Tabriz, Iran. His studies of the nonlinear solitons, Hirota bilinear and trilinear method and Lie symmetric methods characteristics began during his Ph. D. thesis work at the Department of Applied Mathematics, University of Tabriz Subsequently, Dr. Manafian also completed a professor work at the University of Tabriz. He works now at University of Tabriz, Iran.