Oscillations and Resonances.:
This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of charac...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin/Boston, UNITED STATES :
De Gruyter,
2017.
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications ;
v. 23/1. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators. |
| Beschreibung: | 1 online resource (357) : illustrations |
| ISBN: | 3110335689 9783110335682 9783110382723 3110382725 |
Internformat
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| 505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Contents -- |t Introduction -- |t 1 Asymptotic expansions and series -- |t 2 Asymptotic methods for solving nonlinear equations -- |t 3 Perturbation of nonlinear oscillations -- |t 4 Nonlinear oscillator in potential well -- |t 5 Autoresonances in nonlinear systems -- |t 6 Asymptotics for loss of stability -- |t 7 Systems of coupled oscillators -- |t Bibliography -- |t Index. |
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| author | Glebov, Sergey G. |
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| contents | Frontmatter -- Preface -- Contents -- Introduction -- 1 Asymptotic expansions and series -- 2 Asymptotic methods for solving nonlinear equations -- 3 Perturbation of nonlinear oscillations -- 4 Nonlinear oscillator in potential well -- 5 Autoresonances in nonlinear systems -- 6 Asymptotics for loss of stability -- 7 Systems of coupled oscillators -- Bibliography -- Index. |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn985846032 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T14:23:26Z |
| institution | BVB |
| isbn | 3110335689 9783110335682 9783110382723 3110382725 |
| language | English |
| oclc_num | 985846032 |
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| series | De Gruyter series in nonlinear analysis and applications ; |
| series2 | De Gruyter Series in Nonlinear Analysis and applications ; |
| spelling | Glebov, Sergey G. Oscillations and Resonances. Berlin/Boston, UNITED STATES : De Gruyter, 2017. 1 online resource (357) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and applications ; Volume 23/1 Print version record. Frontmatter -- Preface -- Contents -- Introduction -- 1 Asymptotic expansions and series -- 2 Asymptotic methods for solving nonlinear equations -- 3 Perturbation of nonlinear oscillations -- 4 Nonlinear oscillator in potential well -- 5 Autoresonances in nonlinear systems -- 6 Asymptotics for loss of stability -- 7 Systems of coupled oscillators -- Bibliography -- Index. This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators. In English. Nonlinear functional analysis. http://id.loc.gov/authorities/subjects/sh85092325 Analyse fonctionnelle non linéaire. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Nonlinear functional analysis fast Print version: 9783110335545 3110335549 (OCoLC)931647957 De Gruyter series in nonlinear analysis and applications ; v. 23/1. http://id.loc.gov/authorities/names/n92047842 |
| spellingShingle | Glebov, Sergey G. Oscillations and Resonances. De Gruyter series in nonlinear analysis and applications ; Frontmatter -- Preface -- Contents -- Introduction -- 1 Asymptotic expansions and series -- 2 Asymptotic methods for solving nonlinear equations -- 3 Perturbation of nonlinear oscillations -- 4 Nonlinear oscillator in potential well -- 5 Autoresonances in nonlinear systems -- 6 Asymptotics for loss of stability -- 7 Systems of coupled oscillators -- Bibliography -- Index. Nonlinear functional analysis. http://id.loc.gov/authorities/subjects/sh85092325 Analyse fonctionnelle non linéaire. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Nonlinear functional analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85092325 |
| title | Oscillations and Resonances. |
| title_alt | Frontmatter -- Preface -- Contents -- Introduction -- 1 Asymptotic expansions and series -- 2 Asymptotic methods for solving nonlinear equations -- 3 Perturbation of nonlinear oscillations -- 4 Nonlinear oscillator in potential well -- 5 Autoresonances in nonlinear systems -- 6 Asymptotics for loss of stability -- 7 Systems of coupled oscillators -- Bibliography -- Index. |
| title_auth | Oscillations and Resonances. |
| title_exact_search | Oscillations and Resonances. |
| title_full | Oscillations and Resonances. |
| title_fullStr | Oscillations and Resonances. |
| title_full_unstemmed | Oscillations and Resonances. |
| title_short | Oscillations and Resonances. |
| title_sort | oscillations and resonances |
| topic | Nonlinear functional analysis. http://id.loc.gov/authorities/subjects/sh85092325 Analyse fonctionnelle non linéaire. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Nonlinear functional analysis fast |
| topic_facet | Nonlinear functional analysis. Analyse fonctionnelle non linéaire. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Nonlinear functional analysis |
| work_keys_str_mv | AT glebovsergeyg oscillationsandresonances |