## Physics of SolitonsSolitons 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 |

412 | |

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### Common terms and phrases

amplitude antisoliton assume atoms base pairs bonds boundary conditions calculation carrier wave chain Chapter coefﬁcient collective coordinate collision commensurate phase continuum limit approximation corresponds coupling Davydov soliton deﬁned denote density depends derived described determine discommensuration discrete dislocation dispersion relation domain wall dynamics eigenfunctions eigenvalues electrons energy equilibrium excitations expression ferroelectric ﬁbre ﬁeld ﬁnd ﬁnite ﬁrst ﬂuctuations ﬂuid frequency function Hamiltonian inﬁnity integral interaction internal mode introduce inverse scattering transform John Scott Russell KdV equation kink Lagrangian lattice leads linear linearised localised magnetic method molecule Morse potential motion NLS equation nonlinear obtained one-dimensional operator oscillation parameter particles perturbation phonon plane wave plasma polarisation polyacetylene position properties pulse quantum Schršodinger equation shows sine-Gordon equation soliton solution space spatial spin substrate potential sufﬁcient temperature term thermal variables velocity wavevector