Nonlinear Equations with Small Parameter. / Volume 1, : 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...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2017] ©2017 |
Year of Publication: | 2017 |
Language: | English |
Series: | De Gruyter Series in Nonlinear Analysis and Applications ,
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Physical Description: | 1 online resource (XVIII, 339 p.) |
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Tarkhanov, Nikolai N., author. aut http://id.loc.gov/vocabulary/relators/aut Nonlinear Equations with Small Parameter. Volume 1, Oscillations and Resonances. Berlin ; Boston : De Gruyter, [2017] ©2017 1 online resource (XVIII, 339 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 23/1 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Kleine Parameter. Nichtlineare Gleichungen. MATHEMATICS / Differential Equations / General. bisacsh Nonlinear equations. approximate solutions. global asymptotics. small parameter. Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 9783110762495 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 9783110719543 Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications 9783110647099 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 9783110540550 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 9783110625264 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 9783110548204 ZDB-23-DMA EPUB 9783110382723 print 9783110335545 https://doi.org/10.1515/9783110335682 https://www.degruyter.com/isbn/9783110335682 Cover https://www.degruyter.com/document/cover/isbn/9783110335682/original |
language |
English |
format |
eBook |
author |
Tarkhanov, Nikolai N., Tarkhanov, Nikolai N., |
spellingShingle |
Tarkhanov, Nikolai N., Tarkhanov, Nikolai N., Nonlinear Equations with Small Parameter. 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 |
author_facet |
Tarkhanov, Nikolai N., Tarkhanov, Nikolai N., |
author_variant |
n n t nn nnt n n t nn nnt |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Tarkhanov, Nikolai N., |
title |
Nonlinear Equations with Small Parameter. |
title_full |
Nonlinear Equations with Small Parameter. Volume 1, Oscillations and Resonances. |
title_fullStr |
Nonlinear Equations with Small Parameter. Volume 1, Oscillations and Resonances. |
title_full_unstemmed |
Nonlinear Equations with Small Parameter. Volume 1, Oscillations and Resonances. |
title_auth |
Nonlinear Equations with Small Parameter. |
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_new |
Nonlinear Equations with Small Parameter. |
title_sort |
nonlinear equations with small parameter. oscillations and resonances. |
series |
De Gruyter Series in Nonlinear Analysis and Applications , |
series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
publisher |
De Gruyter, |
publishDate |
2017 |
physical |
1 online resource (XVIII, 339 p.) Issued also in print. |
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 |
isbn |
9783110335682 9783110762495 9783110719543 9783110647099 9783110540550 9783110625264 9783110548204 9783110382723 9783110335545 |
issn |
0941-813X ; |
url |
https://doi.org/10.1515/9783110335682 https://www.degruyter.com/isbn/9783110335682 https://www.degruyter.com/document/cover/isbn/9783110335682/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110335682 |
oclc_num |
984625916 |
work_keys_str_mv |
AT tarkhanovnikolain nonlinearequationswithsmallparametervolume1 |
status_str |
n |
ids_txt_mv |
(DE-B1597)213692 (OCoLC)984625916 |
carrierType_str_mv |
cr |
title_part_txt |
Oscillations and Resonances. |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 |
is_hierarchy_title |
Nonlinear Equations with Small Parameter. |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 |
_version_ |
1806144342564274176 |
fullrecord |
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