Physics of Solitons

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Cambridge University Press, Mar 9, 2006 - Mathematics - 422 pages
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Solitons are waves with exceptional stability properties which appear in many areas of physics. The basic properties of solitons are introduced here using examples from macroscopic physics (e.g. blood pressure pulses and fibre optical communications). The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and Bose-Einstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations. Throughout the book the authors emphasise a fresh approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general physics, and classical and quantum mechanics.
 

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Contents

Different classes of solitons
1
the Kortewegde Vries equation
7
the sineGordon equation
42
the nonlinear
75
ion acoustic waves in a plasma
117
Mathematical methods for the study of solitons
139
Collective coordinate method
156
The inversescattering transform
165
Incommensurate phases
235
Solitons in magnetic systems
252
Solitons in conducting polymers
269
Solitons in BoseEinstein condensates
297
Nonlinear excitations in biological molecules
323
Energy localisation and transfer in proteins
326
Nonlinear dynamics and statistical physics of DNA
351
do they exist?
389

Examples in solid state and atomic physics
185
9Asimple model for dislocations in crystals
199
Ferroelectric domain walls
211
Appendices
395
References
412
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