This book shows that the physical phenomena and processes that take place in nature generally have complicated nonlinear features, which leads to nonlinear mathematical models for the real processes. It focuses on the practical issues involved here, as well as the development of methods to investigate the associated nonlinear mathematical problems, including nonlinear wave propagation. It acquaints the reader with a series of methods and approaches that can be applied to a wide class of nonlinear equations. The book also outlines a way in which an uninitiated reader could investigate a new nonlinear equation. Dr Vyacheslav O. Vakhnenko is currently the Chief Scientist of the Division of Geodynamics of Explosion at the Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine. He received his PhD from the Institute of Chemical Physics, Moscow, in 1984, and his DSc from Odessa State University, Ukraine, in 1995. His scientific interests include nonlinear evolution equations, loop-like solitons, integrability, dynamics of nonlinear wave processes in the geophysical medium, and diagnostic methods for heterogeneous media properties by nonlinear long waves. Dr E. J. (John) Parkes worked as a Lecturer at the Department of Mathematics and Statistics of the University of Strathclyde, UK. His work has centred on nonlinear evolution equations and, in particular, integrable systems.