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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
A S Davydov |

ISBN: | 9789401730259 9401730253 |

OCLC Number: | 851393386 |

Description: | 1 online resource (xviii, 319 pages). |

Contents: | I. Collective Excitations in Quasi-Periodical Molecular Structures -- II. Excitations of Solitons in One-Dimensional Molecular Systems -- III. Dynamical Properties of Solitons -- IV. Solitons in Molecular Systems With Nonlinear Intermolecular Interactions -- V. Super-Sound Acoustic Solitons -- VI. Theory of Electron Transfer by Solitons -- VII. Space-Periodic Excitations in Nonlinear Systems -- VIII. Long Waves in Nonlinear Media with Cubic Dispersion -- IX the Nonlinear Sine-Gordon Equation -- X. Some Nonlinear Phenomena in Solids -- XI. Conformal Excitations in One-Dimensional Molecular Systems -- XII. Solitons and Proton Motion in Molecular Systems with Hydrogen Bonds -- XIII. Three-Dimensional Soliton (Polarons) in Ionic Crystal -- Appendix A. Coherent Phonon States in One-Dimensional Systems -- Al. Free Vibrations. Phonons -- A2. Vibrations of Atoms in the Presence of External Force -- A3. Virtual Phonons. Coherent States -- A4. Coherent States: Different Representations -- A5. General Properties of Coherent States -- A6. The Time-Dependent Evolution of Coherent States -- A7. Evaluation of Thermodynamical Averages -- Appendix B. Elementary Information of the Jacobian Elliptic Functions -- Appendix C. Elementary Data on the Jacobi Theta Functions -- C1. Relation of Theta Functions to Elliptic Functions and Integrals -- Appendix D. Solitons and the Molecular Mechanism of the Action of Microwave Radiation on Living Cells -- Appendix E. Subsonic and Supersonic Solitons in Quasi-One-Dimensional Molecular Structures -- E1. Basic Equations -- E2. An Integral Equation for the Case of Dispersion and Anharmonicity -- E3. Subsonic and Supersonic Solutions of the First Kind -- E4. Supersonic Solitons of the Second Kind -- Notes -- Additional Bibliography. |

Series Title: | Mathematics and Its Applications, Soviet Series, 4. |

Responsibility: | by A.S. Davydov. |

### Abstract:

Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory;
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