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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2017]
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
volume 23/1 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FHA01 FHR01 FKE01 FLA01 TUM01 UBW01 UBY01 UPA01 FCO01 URL des Erstveröffentlichers |
| 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-Ressource (XVIII, 335 Seiten) Diagramme |
| ISBN: | 9783110335682 |
| DOI: | 10.1515/9783110335682 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV044343756 | ||
| 003 | DE-604 | ||
| 005 | 20200630 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 170609s2017 |||| o||u| ||||||eng d | ||
| 020 | |a 9783110335682 |9 978-3-11-033568-2 | ||
| 024 | 7 | |a 10.1515/9783110335682 |2 doi | |
| 035 | |a (ZDB-23-DGG)9783110335682 | ||
| 035 | |a (OCoLC)992512966 | ||
| 035 | |a (DE-599)BVBBV044343756 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-Aug4 |a DE-859 |a DE-860 |a DE-20 |a DE-91 |a DE-898 |a DE-739 |a DE-706 |a DE-1046 |a DE-1043 |a DE-858 | ||
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 100 | 1 | |a Glebov, Sergej G. |e Verfasser |0 (DE-588)1132829518 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear Equations with Small Parameter |b Volume 1: Oscillations and resonances |c Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a 1 Online-Ressource (XVIII, 335 Seiten) |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v volume 23/1 | |
| 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 | ||
| 650 | 4 | |a approximate solutions | |
| 650 | 4 | |a global asymptotics | |
| 650 | 4 | |a Kleine Parameter | |
| 650 | 4 | |a Nichtlineare Gleichungen | |
| 650 | 4 | |a Nonlinear equations | |
| 650 | 4 | |a small parameter | |
| 650 | 0 | 7 | |a Schwingungsgleichung |0 (DE-588)4180567-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotische Methode |0 (DE-588)4287476-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Gleichung |0 (DE-588)4455337-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Gleichung |0 (DE-588)4455337-7 |D s |
| 689 | 0 | 1 | |a Schwingungsgleichung |0 (DE-588)4180567-7 |D s |
| 689 | 0 | 2 | |a Asymptotische Methode |0 (DE-588)4287476-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kiselev, Oleg Michajlovič |e Sonstige |0 (DE-588)1132830591 |4 oth | |
| 700 | 1 | |a Tarchanov, Nikolaj Nikolaevič |d 1955-2020 |e Sonstige |0 (DE-588)121160521 |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-3-11-033554-5 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications |v volume 23/1 |w (DE-604)BV005530011 |9 23/1 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9783110335682 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-23-DGG |a ZDB-23-DMA | ||
| 940 | 1 | |q ZDB-23-DMA17 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029746743 | ||
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FAB01 |p ZDB-23-DGG |q FAB_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FAW01 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FHA01 |p ZDB-23-DGG |q FHA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FHR01 |p ZDB-23-DMA |q ZDB-23-DMA17 |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FKE01 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FLA01 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l TUM01 |p ZDB-23-DMA |q TUM_Paketkauf |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l UBW01 |p ZDB-23-DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l UBY01 |p ZDB-23-DMA |q UBY_Paketkauf17 |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l UPA01 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110335682 |l FCO01 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804177579226169344 |
|---|---|
| any_adam_object | |
| author | Glebov, Sergej G. |
| author_GND | (DE-588)1132829518 (DE-588)1132830591 (DE-588)121160521 |
| author_facet | Glebov, Sergej G. |
| author_role | aut |
| author_sort | Glebov, Sergej G. |
| author_variant | s g g sg sgg |
| building | Verbundindex |
| bvnumber | BV044343756 |
| classification_rvk | SK 520 |
| collection | ZDB-23-DGG ZDB-23-DMA |
| ctrlnum | (ZDB-23-DGG)9783110335682 (OCoLC)992512966 (DE-599)BVBBV044343756 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9783110335682 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04757nmm a2200697zcb4500</leader><controlfield tag="001">BV044343756</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200630 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">170609s2017 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110335682</subfield><subfield code="9">978-3-11-033568-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783110335682</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-23-DGG)9783110335682</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)992512966</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044343756</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-Aug4</subfield><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Glebov, Sergej G.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1132829518</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear Equations with Small Parameter</subfield><subfield code="b">Volume 1: Oscillations and resonances</subfield><subfield code="c">Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ; Boston</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">[2017]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XVIII, 335 Seiten)</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">volume 23/1</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">approximate solutions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">global asymptotics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Kleine Parameter</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nichtlineare Gleichungen</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">small parameter</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Schwingungsgleichung</subfield><subfield code="0">(DE-588)4180567-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Asymptotische Methode</subfield><subfield code="0">(DE-588)4287476-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Gleichung</subfield><subfield code="0">(DE-588)4455337-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Gleichung</subfield><subfield code="0">(DE-588)4455337-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Schwingungsgleichung</subfield><subfield code="0">(DE-588)4180567-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Asymptotische Methode</subfield><subfield code="0">(DE-588)4287476-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kiselev, Oleg Michajlovič</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1132830591</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tarchanov, Nikolaj Nikolaevič</subfield><subfield code="d">1955-2020</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)121160521</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-3-11-033554-5</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">volume 23/1</subfield><subfield code="w">(DE-604)BV005530011</subfield><subfield code="9">23/1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="a">ZDB-23-DMA</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-23-DMA17</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029746743</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FAB01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAB_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FHA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FHA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FHR01</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">ZDB-23-DMA17</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FKE01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FLA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">TUM01</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">TUM_Paketkauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">UBW01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">UBY01</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">UBY_Paketkauf17</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110335682</subfield><subfield code="l">FCO01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV044343756 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:50:19Z |
| institution | BVB |
| isbn | 9783110335682 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029746743 |
| oclc_num | 992512966 |
| open_access_boolean | |
| owner | DE-Aug4 DE-859 DE-860 DE-20 DE-91 DE-BY-TUM DE-898 DE-BY-UBR DE-739 DE-706 DE-1046 DE-1043 DE-858 |
| owner_facet | DE-Aug4 DE-859 DE-860 DE-20 DE-91 DE-BY-TUM DE-898 DE-BY-UBR DE-739 DE-706 DE-1046 DE-1043 DE-858 |
| physical | 1 Online-Ressource (XVIII, 335 Seiten) Diagramme |
| psigel | ZDB-23-DGG ZDB-23-DMA ZDB-23-DMA17 ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FHA_PDA_DGG ZDB-23-DMA ZDB-23-DMA17 ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DMA TUM_Paketkauf ZDB-23-DMA UBY_Paketkauf17 ZDB-23-DGG UPA_PDA_DGG ZDB-23-DGG FCO_PDA_DGG |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Glebov, Sergej G. Verfasser (DE-588)1132829518 aut Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov Berlin ; Boston De Gruyter [2017] © 2017 1 Online-Ressource (XVIII, 335 Seiten) Diagramme txt rdacontent c rdamedia cr rdacarrier De Gruyter series in nonlinear analysis and applications volume 23/1 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 approximate solutions global asymptotics Kleine Parameter Nichtlineare Gleichungen Nonlinear equations small parameter Schwingungsgleichung (DE-588)4180567-7 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Nichtlineare Gleichung (DE-588)4455337-7 gnd rswk-swf Nichtlineare Gleichung (DE-588)4455337-7 s Schwingungsgleichung (DE-588)4180567-7 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Kiselev, Oleg Michajlovič Sonstige (DE-588)1132830591 oth Tarchanov, Nikolaj Nikolaevič 1955-2020 Sonstige (DE-588)121160521 oth Erscheint auch als Druck-Ausgabe 978-3-11-033554-5 De Gruyter series in nonlinear analysis and applications volume 23/1 (DE-604)BV005530011 23/1 https://doi.org/10.1515/9783110335682 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Glebov, Sergej G. Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances De Gruyter series in nonlinear analysis and applications approximate solutions global asymptotics Kleine Parameter Nichtlineare Gleichungen Nonlinear equations small parameter Schwingungsgleichung (DE-588)4180567-7 gnd Asymptotische Methode (DE-588)4287476-2 gnd Nichtlineare Gleichung (DE-588)4455337-7 gnd |
| subject_GND | (DE-588)4180567-7 (DE-588)4287476-2 (DE-588)4455337-7 |
| title | Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances |
| title_auth | Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances |
| title_exact_search | Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances |
| title_full | Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| title_fullStr | Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| title_full_unstemmed | Nonlinear Equations with Small Parameter Volume 1: Oscillations and resonances Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| title_short | Nonlinear Equations with Small Parameter |
| title_sort | nonlinear equations with small parameter volume 1 oscillations and resonances |
| title_sub | Volume 1: Oscillations and resonances |
| topic | approximate solutions global asymptotics Kleine Parameter Nichtlineare Gleichungen Nonlinear equations small parameter Schwingungsgleichung (DE-588)4180567-7 gnd Asymptotische Methode (DE-588)4287476-2 gnd Nichtlineare Gleichung (DE-588)4455337-7 gnd |
| topic_facet | approximate solutions global asymptotics Kleine Parameter Nichtlineare Gleichungen Nonlinear equations small parameter Schwingungsgleichung Asymptotische Methode Nichtlineare Gleichung |
| url | https://doi.org/10.1515/9783110335682 |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT glebovsergejg nonlinearequationswithsmallparametervolume1oscillationsandresonances AT kiselevolegmichajlovic nonlinearequationswithsmallparametervolume1oscillationsandresonances AT tarchanovnikolajnikolaevic nonlinearequationswithsmallparametervolume1oscillationsandresonances |