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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Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 |
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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 ,
23/1 |
Online Access: | |
Physical Description: | 1 online resource (XVIII, 339 p.) |
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100 | 1 | |a Tarkhanov, Nikolai N., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Nonlinear Equations with Small Parameter. |n Volume 1, |p Oscillations and Resonances. |
264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2017] | |
264 | 4 | |c ©2017 | |
300 | |a 1 online resource (XVIII, 339 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a De Gruyter Series in Nonlinear Analysis and Applications , |x 0941-813X ; |v 23/1 | |
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 |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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 | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) | |
650 | 4 | |a Kleine Parameter. | |
650 | 4 | |a Nichtlineare Gleichungen. | |
650 | 7 | |a MATHEMATICS / Differential Equations / General. |2 bisacsh | |
653 | |a Nonlinear equations. | ||
653 | |a approximate solutions. | ||
653 | |a global asymptotics. | ||
653 | |a small parameter. | ||
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Plus DeG Package 2017 Part 1 |z 9783110762495 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Plus eBook-Package 2017 |z 9783110719543 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Studies in Nonlinear Analysis and Applications |z 9783110647099 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2017 |z 9783110540550 |o ZDB-23-DGG |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE ENGLISH 2017 |z 9783110625264 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2017 |z 9783110548204 |o ZDB-23-DMA |
776 | 0 | |c EPUB |z 9783110382723 | |
776 | 0 | |c print |z 9783110335545 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9783110335682 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9783110335682 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9783110335682/original |
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912 | |a 978-3-11-064709-9 DG Studies in Nonlinear Analysis and Applications | ||
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912 | |a 978-3-11-076249-5 DG Plus DeG Package 2017 Part 1 |b 2017 | ||
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