Introduction to the Mathematical Physics of Nonlinear Waves

Nonlinear dynamics is a well-established discipline in physics, and this book offers a comprehensive textbook on the basic soliton theory and its applications, especially for crystalline processes. Although primarily mathematical, the author discusses the theory for nonlinear phenomena in a practical environment, paying particular attention to the presence of media where nonlinearity occurs. Written for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods underpinning important new developments in this field, especially as applied to solid-state materials. The updated edition has been extended to emphasize the importance of thermodynamics in a description of modulated crystals and contains new chapters on superconductivity that can be interpreted by the soliton mechanism. It is also updated to include new end-of-chapter problems.