非线性物理科学：偏微分方程与孤波理论

Partial Differential Equations and Solitary Waves Theory is a book that presents newly developed methods for solving PDEs and provides an extensive exposition of the solitary waves theory. Both parts are accessible and self-contained with examples and exercises, making it easy for advanced undergraduate and graduate students in applied mathematics, physics, and engineering to study. Part I deals with the basic concepts of PDEs, one and higher-dimensional heat and wave flow, Laplaces equation, and nonlinear PDEs. Part II focuses on the analysis of solitary waves theory, including its definitions, types of traveling wave solutions, and methods of analysis such as the tanh-coth method and Hirotas bilinear method. This book is a valuable resource for anyone looking to develop their knowledge in mathematics and physics.