Bifurcations in the Generalized Korteweg–de Vries Equation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-02

AUTHORS

S. A. Kashchenko, M. M. Preobrazhenskaya

ABSTRACT

We study the generalized Korteweg–de Vries (KdV) equation and the Korteweg–de Vries–Burgers (KdVB) equation with periodic in the spatial variable boundary conditions. For various values of parameters, in a sufficiently small neighborhood of the zero equilibrium state we construct asymptotics of periodic solutions and invariant tori. Separately we consider the case when the stability spectrum of the zero solution contains a countable number of roots of the characteristic equation. In this case we state a special nonlinear boundary-value problem which plays the role of a normal form and determines the dynamics of the initial problem. More... »

PAGES

49-61

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.3103/s1066369x18020068

DOI

http://dx.doi.org/10.3103/s1066369x18020068

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101521080


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Moscow Engineering Physics Institute", 
          "id": "https://www.grid.ac/institutes/grid.183446.c", 
          "name": [
            "P. G. Demidov Yaroslavl State University, ul. Sovetskaya 14, 150003, Yaroslavl, Russia", 
            "MEPhi National Research Nuclear University, Kashirskoe shosse 31, 115409, Moscow, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kashchenko", 
        "givenName": "S. A.", 
        "id": "sg:person.014005151473.05", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014005151473.05"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Scientific Center", 
          "id": "https://www.grid.ac/institutes/grid.465407.4", 
          "name": [
            "P. G. Demidov Yaroslavl State University, ul. Sovetskaya 14, 150003, Yaroslavl, Russia", 
            "Scientific Center in Chernogolovka of Russian Academy of Sciences, ul. Lesnaya 9, 142432, Chernogolovka, Moscow region, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Preobrazhenskaya", 
        "givenName": "M. M.", 
        "id": "sg:person.012115764364.00", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012115764364.00"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1134/s1064562416030170", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021494274", 
          "https://doi.org/10.1134/s1064562416030170"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562416030170", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021494274", 
          "https://doi.org/10.1134/s1064562416030170"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/14786449508620739", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021858340"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.cnsns.2008.09.020", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026563139"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01164258", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027281761", 
          "https://doi.org/10.1007/bf01164258"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01164258", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027281761", 
          "https://doi.org/10.1007/bf01164258"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s0965542512080040", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035922089", 
          "https://doi.org/10.1134/s0965542512080040"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562410060104", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044255696", 
          "https://doi.org/10.1134/s1064562410060104"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0065-2156(08)70100-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045913525"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/rm1980v035n05abeh001929", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058194689"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/s021812749600059x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062958324"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-02", 
    "datePublishedReg": "2018-02-01", 
    "description": "We study the generalized Korteweg\u2013de Vries (KdV) equation and the Korteweg\u2013de Vries\u2013Burgers (KdVB) equation with periodic in the spatial variable boundary conditions. For various values of parameters, in a sufficiently small neighborhood of the zero equilibrium state we construct asymptotics of periodic solutions and invariant tori. Separately we consider the case when the stability spectrum of the zero solution contains a countable number of roots of the characteristic equation. In this case we state a special nonlinear boundary-value problem which plays the role of a normal form and determines the dynamics of the initial problem.", 
    "genre": "research_article", 
    "id": "sg:pub.10.3103/s1066369x18020068", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1295492", 
        "issn": [
          "0021-3446", 
          "1934-810X"
        ], 
        "name": "Russian Mathematics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "62"
      }
    ], 
    "name": "Bifurcations in the Generalized Korteweg\u2013de Vries Equation", 
    "pagination": "49-61", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "6a250447fc6d7cb2056756bb76df34c0a0b131ea7953338f0261df1b6c9cbb74"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.3103/s1066369x18020068"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1101521080"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.3103/s1066369x18020068", 
      "https://app.dimensions.ai/details/publication/pub.1101521080"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T11:36", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000358_0000000358/records_127426_00000010.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.3103%2FS1066369X18020068"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.3103/s1066369x18020068'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.3103/s1066369x18020068'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.3103/s1066369x18020068'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.3103/s1066369x18020068'


 

This table displays all metadata directly associated to this object as RDF triples.

104 TRIPLES      21 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.3103/s1066369x18020068 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N7f8c94430a5f4986828dc0930feb32a1
4 schema:citation sg:pub.10.1007/bf01164258
5 sg:pub.10.1134/s0965542512080040
6 sg:pub.10.1134/s1064562410060104
7 sg:pub.10.1134/s1064562416030170
8 https://doi.org/10.1016/j.cnsns.2008.09.020
9 https://doi.org/10.1016/s0065-2156(08)70100-5
10 https://doi.org/10.1070/rm1980v035n05abeh001929
11 https://doi.org/10.1080/14786449508620739
12 https://doi.org/10.1142/s021812749600059x
13 schema:datePublished 2018-02
14 schema:datePublishedReg 2018-02-01
15 schema:description We study the generalized Korteweg–de Vries (KdV) equation and the Korteweg–de Vries–Burgers (KdVB) equation with periodic in the spatial variable boundary conditions. For various values of parameters, in a sufficiently small neighborhood of the zero equilibrium state we construct asymptotics of periodic solutions and invariant tori. Separately we consider the case when the stability spectrum of the zero solution contains a countable number of roots of the characteristic equation. In this case we state a special nonlinear boundary-value problem which plays the role of a normal form and determines the dynamics of the initial problem.
16 schema:genre research_article
17 schema:inLanguage en
18 schema:isAccessibleForFree false
19 schema:isPartOf N8d12e742580c47169675cebe790a8b4d
20 Nf43e96beffb1418c913d0e3cce910834
21 sg:journal.1295492
22 schema:name Bifurcations in the Generalized Korteweg–de Vries Equation
23 schema:pagination 49-61
24 schema:productId N6d7b5c49ed0b4cdd90f6c1940554223b
25 N9d330f1ae2fb4b32b82f82324f3a2848
26 Ncd2f81a02273494c8a00569bb74605de
27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101521080
28 https://doi.org/10.3103/s1066369x18020068
29 schema:sdDatePublished 2019-04-11T11:36
30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
31 schema:sdPublisher N058f6493614b4774b4ee8269531d19a4
32 schema:url https://link.springer.com/10.3103%2FS1066369X18020068
33 sgo:license sg:explorer/license/
34 sgo:sdDataset articles
35 rdf:type schema:ScholarlyArticle
36 N058f6493614b4774b4ee8269531d19a4 schema:name Springer Nature - SN SciGraph project
37 rdf:type schema:Organization
38 N398f1f17784a4848ae9f15b5b89dd2f0 rdf:first sg:person.012115764364.00
39 rdf:rest rdf:nil
40 N6d7b5c49ed0b4cdd90f6c1940554223b schema:name readcube_id
41 schema:value 6a250447fc6d7cb2056756bb76df34c0a0b131ea7953338f0261df1b6c9cbb74
42 rdf:type schema:PropertyValue
43 N7f8c94430a5f4986828dc0930feb32a1 rdf:first sg:person.014005151473.05
44 rdf:rest N398f1f17784a4848ae9f15b5b89dd2f0
45 N8d12e742580c47169675cebe790a8b4d schema:volumeNumber 62
46 rdf:type schema:PublicationVolume
47 N9d330f1ae2fb4b32b82f82324f3a2848 schema:name dimensions_id
48 schema:value pub.1101521080
49 rdf:type schema:PropertyValue
50 Ncd2f81a02273494c8a00569bb74605de schema:name doi
51 schema:value 10.3103/s1066369x18020068
52 rdf:type schema:PropertyValue
53 Nf43e96beffb1418c913d0e3cce910834 schema:issueNumber 2
54 rdf:type schema:PublicationIssue
55 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
56 schema:name Mathematical Sciences
57 rdf:type schema:DefinedTerm
58 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
59 schema:name Pure Mathematics
60 rdf:type schema:DefinedTerm
61 sg:journal.1295492 schema:issn 0021-3446
62 1934-810X
63 schema:name Russian Mathematics
64 rdf:type schema:Periodical
65 sg:person.012115764364.00 schema:affiliation https://www.grid.ac/institutes/grid.465407.4
66 schema:familyName Preobrazhenskaya
67 schema:givenName M. M.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012115764364.00
69 rdf:type schema:Person
70 sg:person.014005151473.05 schema:affiliation https://www.grid.ac/institutes/grid.183446.c
71 schema:familyName Kashchenko
72 schema:givenName S. A.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014005151473.05
74 rdf:type schema:Person
75 sg:pub.10.1007/bf01164258 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027281761
76 https://doi.org/10.1007/bf01164258
77 rdf:type schema:CreativeWork
78 sg:pub.10.1134/s0965542512080040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035922089
79 https://doi.org/10.1134/s0965542512080040
80 rdf:type schema:CreativeWork
81 sg:pub.10.1134/s1064562410060104 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044255696
82 https://doi.org/10.1134/s1064562410060104
83 rdf:type schema:CreativeWork
84 sg:pub.10.1134/s1064562416030170 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021494274
85 https://doi.org/10.1134/s1064562416030170
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1016/j.cnsns.2008.09.020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026563139
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1016/s0065-2156(08)70100-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045913525
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1070/rm1980v035n05abeh001929 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058194689
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1080/14786449508620739 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021858340
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1142/s021812749600059x schema:sameAs https://app.dimensions.ai/details/publication/pub.1062958324
96 rdf:type schema:CreativeWork
97 https://www.grid.ac/institutes/grid.183446.c schema:alternateName Moscow Engineering Physics Institute
98 schema:name MEPhi National Research Nuclear University, Kashirskoe shosse 31, 115409, Moscow, Russia
99 P. G. Demidov Yaroslavl State University, ul. Sovetskaya 14, 150003, Yaroslavl, Russia
100 rdf:type schema:Organization
101 https://www.grid.ac/institutes/grid.465407.4 schema:alternateName Scientific Center
102 schema:name P. G. Demidov Yaroslavl State University, ul. Sovetskaya 14, 150003, Yaroslavl, Russia
103 Scientific Center in Chernogolovka of Russian Academy of Sciences, ul. Lesnaya 9, 142432, Chernogolovka, Moscow region, Russia
104 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...