Nonlinear mathematical physics methods

Author: Lou Senyue, Tang Xiaoyan
Publisher:
Publish Date: 2006-12-01
Features: This book explores how to develop and extend powerful fundamental methods applicable in linear science to nonlinear science. It comprehensively and systematically discusses new research methods established by the authors and their research group in recent years, such as multilinear separation of variables, functional separation of variables, derivative-related functional separation of variables, deformation mapping methods, non-average methods for equation derivation, and more. The book also systematically introduces other important methods and their new developments in the study of rigorous solutions in nonlinear mathematical physics, such as finite and infinite domain scattering methods, formal separation of variables, singularity analysis, symmetry reduction methods, Darboux transformation methods, and Hata direct methods, etc. Using these methods, the book provides a detailed description of various localized excitation modes and their interactions in nonlinear systems. This book can serve as a textbook for senior undergraduate students in physics and mathematics departments of universities and colleges, as well as a foundational course textbook for graduate students in related fields. It is also a valuable reference for researchers in nonlinear science fields such as physics, mathematics, mechanics, computer science, atmospheric and oceanic sciences, etc.