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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.
Preface Preface to the 1st edition 1 Introduction: nonlinearity and elliptic functions in classical mechanics 2 Wave propagation, singularities and boundaries 3 Order variables for structural phase transition 4 Soft modes of lattice displacements 5 Nonlinearity development in crystals: Korteweg-deVries’ equation for collective order variables and the complex potential 6 Soliton mobility in time-temperature conversion for thermal processes: Riccati’s theorem 7 Toda’s lattice of correlation potentials 8 Scattering dynamics in the soliton lattice 9 Pseudopotentials and sine-Gordon equation: topological correlations in domain structure 10 Trigonal structural transitions: domain stability in topological order 11 Soliton theory of superconducting transitions 12 Irreducible thermodynamics of superconducting phase transitions