Premable 1. Introductory concepts 2. Phase transitions and criticality 3. Elementary excitations in solids 4. Quantum field theory background 5. The method of coherent structures (MCS) 6. The physical application of MCS 7. Mathematical methods and results 8. Concusions 6 appendices

Solitons have been of considerable interest to mathematicians since their discovery by Kruskal and Zabusky. This book brings together several aspects of soliton theory currently only available in research papers. Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ∂ method. Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Abstract Nonlinear physics has grown from a collection of exotic examples of nonstandard behavior to an all-embracing scientific methodology. Many examples come from condensed matter physics. This book presents a unified view of many-body condensed matter systems as essentially nonlinear structures capable of exhibiting such features as chaos, coherence, solution formation and phase transitions. The book provides an overview of nonlinear phenomena in science, introduces phase transitions and criticality, and includes a comprehensive exposition of methods and results in the analysis of nonlinear differential equations. To equip the reader with concrete skills in tackling nonlinear problems in physics, the authors also analyze important applications such as metamagnetism, superconductivity, the Hubbard Hamiltonian and the multielectron atom. The book can serve as both a compendium of facts and references related to nonlinear condensed matter physics and a practical introduction to current research methods and the field in general.