Bifurcation, stability and symmetry of nonlinear waves View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1987-09

AUTHORS

S. Thiesen, H. Thomas

ABSTRACT

The bifurcation of wave-like spatio-temporal structures due to a hard-mode instability at non-zero wave number is investigated for a simple class of driven systems in one space dimension. We find generically a bifurcation of two branches of waves, travelling waves and standing waves, characterized by nontrivial subgroups of the symmetry group of the system. If both branches are supercritical, the wave with the larger amplitude is found to be stable. In all other cases, both waves are unstable for small amplitudes. At the common boundary of the stability regions of the two wave types in parameter space we find a bifurcation of a branch of modulated waves involving two independent frequencies, connecting the branches of travelling waves and standing waves. More... »

PAGES

397-408

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01303728

DOI

http://dx.doi.org/10.1007/bf01303728

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035074992


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/2008/09", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0911", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Maritime Engineering", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institut f\u00fcr Physik, Universit\u00e4t Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland", 
          "id": "http://www.grid.ac/institutes/grid.6612.3", 
          "name": [
            "Institut f\u00fcr Physik, Universit\u00e4t Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Thiesen", 
        "givenName": "S.", 
        "id": "sg:person.013607711102.35", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013607711102.35"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institut f\u00fcr Physik, Universit\u00e4t Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland", 
          "id": "http://www.grid.ac/institutes/grid.6612.3", 
          "name": [
            "Institut f\u00fcr Physik, Universit\u00e4t Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Thomas", 
        "givenName": "H.", 
        "id": "sg:person.0711120037.13", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0711120037.13"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01323697", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007292437", 
          "https://doi.org/10.1007/bf01323697"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-81291-0_35", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016879167", 
          "https://doi.org/10.1007/978-3-642-81291-0_35"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0087456", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037501220", 
          "https://doi.org/10.1007/bfb0087456"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-12675-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024790330", 
          "https://doi.org/10.1007/3-540-12675-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4684-9336-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017457124", 
          "https://doi.org/10.1007/978-1-4684-9336-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-68304-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005509662", 
          "https://doi.org/10.1007/978-3-642-68304-6"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1987-09", 
    "datePublishedReg": "1987-09-01", 
    "description": "The bifurcation of wave-like spatio-temporal structures due to a hard-mode instability at non-zero wave number is investigated for a simple class of driven systems in one space dimension. We find generically a bifurcation of two branches of waves, travelling waves and standing waves, characterized by nontrivial subgroups of the symmetry group of the system. If both branches are supercritical, the wave with the larger amplitude is found to be stable. In all other cases, both waves are unstable for small amplitudes. At the common boundary of the stability regions of the two wave types in parameter space we find a bifurcation of a branch of modulated waves involving two independent frequencies, connecting the branches of travelling waves and standing waves.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf01303728", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1285002", 
        "issn": [
          "0722-3277", 
          "1431-584X"
        ], 
        "name": "Zeitschrift f\u00fcr Physik B Condensed Matter", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "65"
      }
    ], 
    "keywords": [
      "hard mode instability", 
      "nonlinear waves", 
      "symmetry group", 
      "space dimensions", 
      "parameter space", 
      "stability region", 
      "wave number", 
      "simple class", 
      "wave type", 
      "spatio-temporal structure", 
      "nontrivial subgroup", 
      "bifurcation", 
      "independent frequencies", 
      "common boundary", 
      "small amplitude", 
      "waves", 
      "large amplitude", 
      "symmetry", 
      "amplitude", 
      "branches", 
      "space", 
      "class", 
      "system", 
      "instability", 
      "dimensions", 
      "boundaries", 
      "stability", 
      "number", 
      "structure", 
      "cases", 
      "frequency", 
      "types", 
      "region", 
      "subgroups", 
      "group"
    ], 
    "name": "Bifurcation, stability and symmetry of nonlinear waves", 
    "pagination": "397-408", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1035074992"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01303728"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01303728", 
      "https://app.dimensions.ai/details/publication/pub.1035074992"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-10-01T06:27", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221001/entities/gbq_results/article/article_190.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf01303728"
  }
]
 

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.10.1007/bf01303728'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf01303728'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01303728'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01303728'


 

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

123 TRIPLES      21 PREDICATES      66 URIs      52 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01303728 schema:about anzsrc-for:09
2 anzsrc-for:0911
3 schema:author N76e418ad95454f0a873fd622207e60bc
4 schema:citation sg:pub.10.1007/3-540-12675-9
5 sg:pub.10.1007/978-1-4684-9336-8
6 sg:pub.10.1007/978-3-642-68304-6
7 sg:pub.10.1007/978-3-642-81291-0_35
8 sg:pub.10.1007/bf01323697
9 sg:pub.10.1007/bfb0087456
10 schema:datePublished 1987-09
11 schema:datePublishedReg 1987-09-01
12 schema:description The bifurcation of wave-like spatio-temporal structures due to a hard-mode instability at non-zero wave number is investigated for a simple class of driven systems in one space dimension. We find generically a bifurcation of two branches of waves, travelling waves and standing waves, characterized by nontrivial subgroups of the symmetry group of the system. If both branches are supercritical, the wave with the larger amplitude is found to be stable. In all other cases, both waves are unstable for small amplitudes. At the common boundary of the stability regions of the two wave types in parameter space we find a bifurcation of a branch of modulated waves involving two independent frequencies, connecting the branches of travelling waves and standing waves.
13 schema:genre article
14 schema:isAccessibleForFree false
15 schema:isPartOf Ne5c0e784c96f477bb0ad95f9bbb0753a
16 Ned8b1391722e47f3beb1c7741b87a3c3
17 sg:journal.1285002
18 schema:keywords amplitude
19 bifurcation
20 boundaries
21 branches
22 cases
23 class
24 common boundary
25 dimensions
26 frequency
27 group
28 hard mode instability
29 independent frequencies
30 instability
31 large amplitude
32 nonlinear waves
33 nontrivial subgroup
34 number
35 parameter space
36 region
37 simple class
38 small amplitude
39 space
40 space dimensions
41 spatio-temporal structure
42 stability
43 stability region
44 structure
45 subgroups
46 symmetry
47 symmetry group
48 system
49 types
50 wave number
51 wave type
52 waves
53 schema:name Bifurcation, stability and symmetry of nonlinear waves
54 schema:pagination 397-408
55 schema:productId N6d2c620f138c4532aba9f0a28d21b6b5
56 Ndd24226f9b114c24a70c55ce859e13e9
57 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035074992
58 https://doi.org/10.1007/bf01303728
59 schema:sdDatePublished 2022-10-01T06:27
60 schema:sdLicense https://scigraph.springernature.com/explorer/license/
61 schema:sdPublisher Nb6e68d201cfb4b7cb4c716695702fb5e
62 schema:url https://doi.org/10.1007/bf01303728
63 sgo:license sg:explorer/license/
64 sgo:sdDataset articles
65 rdf:type schema:ScholarlyArticle
66 N45df2c7b041542fdba1d4663d6d3f4e3 rdf:first sg:person.0711120037.13
67 rdf:rest rdf:nil
68 N6d2c620f138c4532aba9f0a28d21b6b5 schema:name dimensions_id
69 schema:value pub.1035074992
70 rdf:type schema:PropertyValue
71 N76e418ad95454f0a873fd622207e60bc rdf:first sg:person.013607711102.35
72 rdf:rest N45df2c7b041542fdba1d4663d6d3f4e3
73 Nb6e68d201cfb4b7cb4c716695702fb5e schema:name Springer Nature - SN SciGraph project
74 rdf:type schema:Organization
75 Ndd24226f9b114c24a70c55ce859e13e9 schema:name doi
76 schema:value 10.1007/bf01303728
77 rdf:type schema:PropertyValue
78 Ne5c0e784c96f477bb0ad95f9bbb0753a schema:volumeNumber 65
79 rdf:type schema:PublicationVolume
80 Ned8b1391722e47f3beb1c7741b87a3c3 schema:issueNumber 3
81 rdf:type schema:PublicationIssue
82 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
83 schema:name Engineering
84 rdf:type schema:DefinedTerm
85 anzsrc-for:0911 schema:inDefinedTermSet anzsrc-for:
86 schema:name Maritime Engineering
87 rdf:type schema:DefinedTerm
88 sg:journal.1285002 schema:issn 0722-3277
89 1431-584X
90 schema:name Zeitschrift für Physik B Condensed Matter
91 schema:publisher Springer Nature
92 rdf:type schema:Periodical
93 sg:person.013607711102.35 schema:affiliation grid-institutes:grid.6612.3
94 schema:familyName Thiesen
95 schema:givenName S.
96 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013607711102.35
97 rdf:type schema:Person
98 sg:person.0711120037.13 schema:affiliation grid-institutes:grid.6612.3
99 schema:familyName Thomas
100 schema:givenName H.
101 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0711120037.13
102 rdf:type schema:Person
103 sg:pub.10.1007/3-540-12675-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024790330
104 https://doi.org/10.1007/3-540-12675-9
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/978-1-4684-9336-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017457124
107 https://doi.org/10.1007/978-1-4684-9336-8
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/978-3-642-68304-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005509662
110 https://doi.org/10.1007/978-3-642-68304-6
111 rdf:type schema:CreativeWork
112 sg:pub.10.1007/978-3-642-81291-0_35 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016879167
113 https://doi.org/10.1007/978-3-642-81291-0_35
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/bf01323697 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007292437
116 https://doi.org/10.1007/bf01323697
117 rdf:type schema:CreativeWork
118 sg:pub.10.1007/bfb0087456 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037501220
119 https://doi.org/10.1007/bfb0087456
120 rdf:type schema:CreativeWork
121 grid-institutes:grid.6612.3 schema:alternateName Institut für Physik, Universität Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
122 schema:name Institut für Physik, Universität Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
123 rdf:type schema:Organization
 




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


...