Introduction to the Mathematical Physics of Nonlinear Waves

Nonlinear physics is a well established discipline of physics, for which this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the author discusses the theory for nonlinear phenomena in the practical environment to be understood with knowledge at upper-undergraduate level, paying particular attention to the presence of media where nonlinearity takes place. In this book, nonlinear dynamics is discussed as being restricted by practical surroundings, reviewing representative cases for physical reality, then proceeding via general theory to its applications. This book addresses the mathematical theory with respect to the past development, however it implies possible theoretical innovations on many issues, providing a stimulating reference for students and researchers. This book was written for students at upper-undergraduate and graduate levels, as a textbook for upgraded physics courses of nonlinear physics. Nevertheless, nonlinear mathematics is dominated by hyperbolic and elliptic functions, which are relatively unfamiliar topics in the traditional physics curriculum. From the pedagogical viewpoint, included is a short account of elliptic functions as a prerequisite to this book.