Behavior for Large Time of a Two-Component Chain of Harmonic Oscillators

We consider a model consisting of two semi-infinite chains of harmonic oscillators with a special particle subject to a harmonic external potential.We study the Cauchy problem for this model. The main goal is to derive the dispersive bounds for the solutions in the energy weighted norms.

Saved in:
Bibliographic Details
Published inRussian journal of mathematical physics Vol. 25; no. 4; pp. 470 - 491
Main Author Dudnikova, T.V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2018
Springer Nature B.V
Subjects
Cauchy problems
Chains
Harmonic oscillators
Mathematical and Computational Physics
Norms
Physics
Physics and Astronomy
Theoretical
Online AccessGet full text

Cover

Abstract We consider a model consisting of two semi-infinite chains of harmonic oscillators with a special particle subject to a harmonic external potential.We study the Cauchy problem for this model. The main goal is to derive the dispersive bounds for the solutions in the energy weighted norms.
AbstractList We consider a model consisting of two semi-infinite chains of harmonic oscillators with a special particle subject to a harmonic external potential.We study the Cauchy problem for this model. The main goal is to derive the dispersive bounds for the solutions in the energy weighted norms.
Author Dudnikova, T.V.
Author_xml – sequence: 1
  givenname: T.V.
  surname: Dudnikova
  fullname: Dudnikova, T.V.
  email: tdudnikov@mail.ru
  organization: M.V. Keldysh Institute of Applied Mathematics RAS
BookMark eNp9kNFLwzAQxoNMcJv-Ab4VfK7mmqRNH7WoFQZ7cD6XNEu2jDaZSaf435syQVD04biD7_vdd9wMTayzCqFLwNcAhN48A86hzDAHjinGLDtBU2CMpXlO-CTOUU5H_QzNQthhnONonKL6Tm3Fm3E-0bEWwm9UsjK9SpxORLJ6d2nl-n3MskNSbYWxo1AL3ztrZLIM0nSdGJwP5-hUiy6oi68-Ry8P96uqThfLx6fqdpFKAvmQasCEli3lJWOgMeGE0TWTWOoWCqpJxrTgBc_bdQEyI2VbEqoLzklONOZCkjm6Ou7de_d6UGFodu7gbYxsMmCUjPtpdMHRJb0LwSvd7L3phf9oADfjw5pfD4tM8YORZhCDcXbwwnT_ktmRDDHFbpT_vulv6BPdJ3zJ
CitedBy_id crossref_primary_10_20948_prepr_2018_254
crossref_primary_10_4213_tm4054
crossref_primary_10_1134_S1995080221060068
crossref_primary_10_1134_S0081543820010137
Cites_doi 10.1215/S0012-7094-79-04631-3
10.1080/00036810601074321
10.1080/00036810108841007
10.1134/S1061920808040031
10.1063/1.3005597
10.1016/j.jmaa.2009.01.028
10.1063/1.4979629
10.1080/03605300500361529
10.1007/s10958-016-3084-7
ContentType Journal Article
Copyright Pleiades Publishing, Ltd. 2018
Copyright Springer Science & Business Media 2018
Copyright_xml – notice: Pleiades Publishing, Ltd. 2018
– notice: Copyright Springer Science & Business Media 2018
DBID AAYXX
CITATION
DOI 10.1134/S1061920818040052
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Physics
EISSN 1555-6638
EndPage 491
ExternalDocumentID 10_1134_S1061920818040052
GroupedDBID -5F
-5G
-BR
-EM
-Y2
-~C
.VR
06D
0R~
0VY
123
1N0
29~
2J2
2JN
2JY
2KG
2KM
2LR
2VQ
2~H
30V
4.4
408
40D
40E
5VS
6NX
95-
95.
95~
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSNA
ACZOJ
ADHHG
ADHIR
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEBTG
AEFQL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AENEX
AEOHA
AEPYU
AETLH
AEVLU
AEXYK
AFBBN
AFGCZ
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHSBF
AHYZX
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARMRJ
ASPBG
AVWKF
AXYYD
AZFZN
B-.
BA0
BDATZ
BGNMA
BSONS
CAG
COF
CS3
CSCUP
DDRTE
DNIVK
DPUIP
DU5
EBLON
EBS
EIOEI
EJD
ESBYG
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
H13
HF~
HG6
HLICF
HMJXF
HRMNR
HVGLF
HZ~
IJ-
IKXTQ
IWAJR
IXD
I~X
I~Z
J-C
JBSCW
JZLTJ
KOV
LLZTM
M4Y
MA-
N2Q
NB0
NPVJJ
NQJWS
NU0
O9-
O93
O9J
P2P
P9T
PF0
PT4
QOS
R89
R9I
RIG
RNS
ROL
RSV
S16
S1Z
S27
S3B
SAP
SDH
SHX
SISQX
SJYHP
SNE
SNPRN
SNX
SOHCF
SOJ
SPH
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
TSG
TUC
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WK8
XU3
YLTOR
ZMTXR
~A9
AAPKM
AAYXX
ABDBE
ABFSG
ACSTC
ADHKG
AEZWR
AFDZB
AFHIU
AFOHR
AGQPQ
AHPBZ
AHWEU
AIXLP
ATHPR
CITATION
ABRTQ
ID FETCH-LOGICAL-c316t-f10349b489551f038354d5c0cfb174f325fa8786bd71c239b934f788363f08ac3
IEDL.DBID AGYKE
ISSN 1061-9208
IngestDate Sun Jul 13 05:29:11 EDT 2025
Tue Jul 01 01:57:34 EDT 2025
Thu Apr 24 23:06:43 EDT 2025
Fri Feb 21 02:36:22 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 4
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c316t-f10349b489551f038354d5c0cfb174f325fa8786bd71c239b934f788363f08ac3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2154310344
PQPubID 2043707
PageCount 22
ParticipantIDs proquest_journals_2154310344
crossref_primary_10_1134_S1061920818040052
crossref_citationtrail_10_1134_S1061920818040052
springer_journals_10_1134_S1061920818040052
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2018-10-01
PublicationDateYYYYMMDD 2018-10-01
PublicationDate_xml – month: 10
  year: 2018
  text: 2018-10-01
  day: 01
PublicationDecade 2010
PublicationPlace Moscow
PublicationPlace_xml – name: Moscow
– name: New York
PublicationTitle Russian journal of mathematical physics
PublicationTitleAbbrev Russ. J. Math. Phys
PublicationYear 2018
Publisher Pleiades Publishing
Springer Nature B.V
Publisher_xml – name: Pleiades Publishing
– name: Springer Nature B.V
References Dudnikova (CR2) 2008; 15
Vainberg (CR11) 1974; 30
Dudnikova (CR5) 2018; 301
Dudnikova (CR4) 2017; 58
Shaban, Vainberg (CR10) 2001; 80
Islami, Vainberg (CR6) 2006; 31
Dudnikova (CR3) 2016; 219
Cuccagna (CR1) 2009; 354
Pelinosky, Stefanov (CR9) 2008; 49
Jensen, Kato (CR7) 1979; 46
Komech, Kopylova, Kunze (CR8) 2006; 85
T.V. Dudnikova (4471_CR4) 2017; 58
T.V. Dudnikova (4471_CR2) 2008; 15
W. Shaban (4471_CR10) 2001; 80
T.V. Dudnikova (4471_CR3) 2016; 219
A.I. Komech (4471_CR8) 2006; 85
H. Islami (4471_CR6) 2006; 31
T.V. Dudnikova (4471_CR5) 2018; 301
A. Jensen (4471_CR7) 1979; 46
S. Cuccagna (4471_CR1) 2009; 354
D.E. Pelinosky (4471_CR9) 2008; 49
B.R. Vainberg (4471_CR11) 1974; 30
References_xml – volume: 301
  start-page: 82
  year: 2018
  end-page: 97
  ident: CR5
  article-title: Large-Time Behavior of the Infinite System of Harmonic Oscillators on the Half-Line
  publication-title: Complex Analysis, Mathematical Physics, and Applications, Collected papers, Proc. Steklov Inst. Math.
– volume: 46
  start-page: 583
  year: 1979
  end-page: 611
  ident: CR7
  article-title: Spectral Properties of Schrodinger Operators and Time-Decay of the Wave Functions
  publication-title: Duke Math. J.
  doi: 10.1215/S0012-7094-79-04631-3
– volume: 85
  start-page: 1487
  issue: 12
  year: 2006
  end-page: 1508
  ident: CR8
  article-title: Dispersive Estimates for 1D Discrete Schrodinger and Klein–Gordon Equations
  publication-title: Appl. Anal.
  doi: 10.1080/00036810601074321
– volume: 80
  start-page: 525
  year: 2001
  end-page: 556
  ident: CR10
  article-title: Radiation Conditions for the Difference Schrödinger Operators
  publication-title: Appl. Anal.
  doi: 10.1080/00036810108841007
– volume: 15
  start-page: 460
  issue: 4
  year: 2008
  end-page: 472
  ident: CR2
  article-title: On the Asymptotical Normality of Statistical Solutions for Harmonic Crystals in Half-Space
  publication-title: Russ. J. Math. Phys.
  doi: 10.1134/S1061920808040031
– volume: 30
  start-page: 139
  year: 1974
  end-page: 158
  ident: CR11
  article-title: Behavior for Large Time of Solutions of the Klein–Gordon Equation
  publication-title: Trans. Moscow Math. Soc.
– volume: 49
  start-page: 113501
  issue: 11
  year: 2008
  ident: CR9
  article-title: On the Spectral Theory and Dispersive Estimates for a Discrete Schrödinger Equation in One Dimension
  publication-title: J. Math. Phys.
  doi: 10.1063/1.3005597
– volume: 354
  start-page: 594
  year: 2009
  end-page: 605
  ident: CR1
  article-title: Continuity of Wave Operators in ℤ
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2009.01.028
– volume: 58
  start-page: 043301
  issue: 4
  year: 2017
  ident: CR4
  article-title: On Convergence to Equilibrium for One-Dimensional Chain of Harmonic Oscillators on the Half-Line
  publication-title: J. Math. Phys.
  doi: 10.1063/1.4979629
– volume: 31
  start-page: 397
  issue: 3
  year: 2006
  end-page: 416
  ident: CR6
  article-title: Large Time Behavoir of the Solutions to Difference Wave Operators
  publication-title: Comm. Partial Differential Equations
  doi: 10.1080/03605300500361529
– volume: 219
  start-page: 69
  issue: 1
  year: 2016
  end-page: 85
  ident: CR3
  article-title: Long-Time Asymptotics of Solutions to a Hamiltonian System on a Lattice
  publication-title: Journal of Mathematical Sciences
  doi: 10.1007/s10958-016-3084-7
– volume: 354
  start-page: 594
  year: 2009
  ident: 4471_CR1
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2009.01.028
– volume: 46
  start-page: 583
  year: 1979
  ident: 4471_CR7
  publication-title: Duke Math. J.
  doi: 10.1215/S0012-7094-79-04631-3
– volume: 85
  start-page: 1487
  issue: 12
  year: 2006
  ident: 4471_CR8
  publication-title: Appl. Anal.
  doi: 10.1080/00036810601074321
– volume: 30
  start-page: 139
  year: 1974
  ident: 4471_CR11
  publication-title: Trans. Moscow Math. Soc.
– volume: 15
  start-page: 460
  issue: 4
  year: 2008
  ident: 4471_CR2
  publication-title: Russ. J. Math. Phys.
  doi: 10.1134/S1061920808040031
– volume: 219
  start-page: 69
  issue: 1
  year: 2016
  ident: 4471_CR3
  publication-title: Journal of Mathematical Sciences
  doi: 10.1007/s10958-016-3084-7
– volume: 31
  start-page: 397
  issue: 3
  year: 2006
  ident: 4471_CR6
  publication-title: Comm. Partial Differential Equations
  doi: 10.1080/03605300500361529
– volume: 58
  start-page: 043301
  issue: 4
  year: 2017
  ident: 4471_CR4
  publication-title: J. Math. Phys.
  doi: 10.1063/1.4979629
– volume: 49
  start-page: 113501
  issue: 11
  year: 2008
  ident: 4471_CR9
  publication-title: J. Math. Phys.
  doi: 10.1063/1.3005597
– volume: 301
  start-page: 82
  year: 2018
  ident: 4471_CR5
  publication-title: Complex Analysis, Mathematical Physics, and Applications, Collected papers, Proc. Steklov Inst. Math.
– volume: 80
  start-page: 525
  year: 2001
  ident: 4471_CR10
  publication-title: Appl. Anal.
  doi: 10.1080/00036810108841007
SSID ssj0060804
Score 2.1454127
Snippet We consider a model consisting of two semi-infinite chains of harmonic oscillators with a special particle subject to a harmonic external potential.We study...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 470
SubjectTerms Cauchy problems
Chains
Harmonic oscillators
Mathematical and Computational Physics
Norms
Physics
Physics and Astronomy
Theoretical
Title Behavior for Large Time of a Two-Component Chain of Harmonic Oscillators
URI https://link.springer.com/article/10.1134/S1061920818040052
https://www.proquest.com/docview/2154310344
Volume 25
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LSwMxEB6kRfBifWJ9kYMnJXW3yW6zxyLW4vNgC_W0JGmCorbSB4K_3slu1mJ9QM_JZh8zmflmZ_INwFGSGGOVUVRaqSi3NqQyDBNqOPrahkWhZ-fWbm7jdpdf9qKeP8c9Lqrdi5RkZqnzviP89N4FL0ndUbA5xYvQ7pYRfgS8BOXmxcPVeWGAYwRBWTIZ51N3gU9m_rrId3c0w5hzadHM27Qq0CmeMy8yea5NJ6qmP-YoHBd8kTVY9eiTNHN1WYclM9iAikeixO_z8QYsZ4WherwJbU-gOCKIbsm1qxsn7tgIGVoiSed9SJ1FGQ7Qd5GzR_k0cANtOXp1lLvkDh0s6pnr6LMF3dZ556xNffcFqlkYT6gNHXWN4iJBUGUD5v4Q9SMdaKswirGsHlkpGiJW_Uao6yxRCeMWA2oWMxsIqdk2lAZ4-x0giYmktoYJE2gemVgicJBCGCWENojxqhAUQki1pyZ3HTJe0ixEYTz98c2qcPx1yVvOy_Hf5P1CsqnfouMUsQ53TdY4r8JJIajZ8J-L7S40ew9WEGLlDLrhPpQmo6k5QBgzUYdebT8B5Rnigw
linkProvider Springer Nature
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLYQCMGFN2IwIAdOoEC7pF16nKZBYRscGBKcqiQkAgEb2kNI_HqcNgXxlDgnTR927M-18xlgL0mMscooKq1UlFsbUhmGCTUcfW3dotDzc2vd8zi94mfX0bU_xz0qq93LlGRuqYu-I_zo0gUvSc1RsDnFi9DuznAMwVGtZxonN-1WaYBjBEF5MhnnU3eBT2b-uMhnd_SBMb-kRXNvc7wIvfI5iyKTh8PJWB3q1y8Ujv98kSVY8OiTNAp1WYYp01-BRY9Eid_noxWYzQtD9WgVUk-gOCSIbknH1Y0Td2yEDCyRpPcyoM6iDProu0jzTt733UAqh0-OcpdcoINFPXMdfdbg6rjVa6bUd1-gmoXxmNrQUdcoLhIEVTZg7g_RbaQDbRVGMZbVIitFXcTqth7qGktUwrjFgJrFzAZCarYO0328_QaQxERSW8OECTSPTCwROEghjBJCG8R4FQhKIWTaU5O7DhmPWR6iMJ59-2YV2H-_5Lng5fhrcrWUbOa36ChDrMNdkzXOK3BQCupj-NfFNv81exfm0l63k3VOz9tbMI9wq2DTDaswPR5OzDZCmrHa8Sr8BrGU5XI
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB5kRfHiW1yfOXhSou0m7aZHUdf1Laigp5pkExS1K7sVwV_vpE0VnyCe82o7k8w3nck3ACtJYoxVRlFppaLc2pDKMEyo4WhrmxaFXtxbOzqO2xd8_zK69HVO-1W2exWSLO80OJamLN947Fhfg4RvnDlHJmk4OjanhBGewYPcUdvVYHBz9-pgpzqMYwRERWAZ-1M3wAc2v53ko2l6x5ufQqSF5WmNwXX1zGXCyd36U67W9csnOsd_vNQ4jHpUSjZLNZqAAZNNwphHqMTv__4kDBUJo7o_BW1PrNgjiHrJocsnJ-46CelaIsn5c5e6k6ab4fJk60beZq6hLXsPjoqXnKDhRf1zlX6m4aK1c77Vpr4qA9UsjHNqQ0dpo7hIEGzZgLk_R51IB9oq9G4sa0RWiqaIVacZ6gZLVMK4RUebxcwGQmo2A7UMl58FkphIamuYMIHmkYklAgophFFCaIPYrw5BJZBUe8pyVznjPi1cF8bTL9-sDqtvQx5Lvo7fOi9UUk791u2niIG4K77GeR3WKqG9N_842dyfei_D8Ol2Kz3cOz6YhxFEYSXJbrgAtbz3ZBYR6eRqyWvzKyqc7lY
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Behavior+for+Large+Time+of+a+Two-Component+Chain+of+Harmonic+Oscillators&rft.jtitle=Russian+journal+of+mathematical+physics&rft.au=Dudnikova%2C+T.V.&rft.date=2018-10-01&rft.pub=Pleiades+Publishing&rft.issn=1061-9208&rft.eissn=1555-6638&rft.volume=25&rft.issue=4&rft.spage=470&rft.epage=491&rft_id=info:doi/10.1134%2FS1061920818040052&rft.externalDocID=10_1134_S1061920818040052
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1061-9208&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1061-9208&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1061-9208&client=summon