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Introduction to the Mathematical Physics of Nonlinear Waves (Second Edition)

Minoru Fujimoto


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.

About Editors

Minoru Fujimoto is a retired professor from the University of Guelph, Canada, where he conducted research in the field of magnetic resonance studies on structural phase transitions in crystals which has currently been extended to theoretical work with soliton dynamics especially as applied to crystalline condensed matter systems. He is the author of numerous papers and several books including Physics of Classical Electromagnetism and Thermodynamics of Crystalline States (Springer); Introduction to Mathematical Physics of Nonlinear Waves and Solitons in Crystalline Processes (IOP Publishing). He lives in Mississauga, Ontario.

Table of Contents

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


Hardback ISBN: 9780750337571

Ebook ISBN: 9780750337595

DOI: 10.1088/978-0-7503-3759-5

Publisher: Institute of Physics Publishing


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