Group properties of the acoustic differential equation:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Taylor & Francis
1995
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 151 S. |
| ISBN: | 0748402802 |
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MARC
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Record in the Search Index
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| adam_text | GROUP PROPERTIES OF THE ACOUSTIC EQUATION LEONID V. POLUYANOV, ANTONIO
AGUILAR AND MIGUEL GONZALEZ TANCIS PUBLISHERS SINCE 1798 CONTENTS
PREFACE VII SYMBOLS IX INTRODUCTION XIII 1 SYMMETRY OF THE MAIN EQUATION
1 1.1 SYMMETRY OPERATORS OF ACOUSTIC EQUATIONS. MAIN OPERATOR EQUATION 2
1.2 CENTRAL SYSTEM OF DIFFERENTIAL EQUATIONS 2 1.3 SYMMETRY OPERATORS
FOR HOMOGENEOUS MEDIA 5 1.4 NON-HOMOGENEOUS MEDIA WITH DIFFERENT
SYMMETRIES 8 1.4.1 MEDIA WITH TRANSLATIONAL SYMMETRY 8 1.4.2 MEDIA WITH
DILATATIONAL SYMMETRY 9 1.4.3 MEDIA WITH ROTATIONAL SYMMETRY 10 1.4.4
MEDIA WITH ROTATIONAL AND DILATATIONAL SYMMETRY 11 1.4.5 MEDIA WITH
SPIRAL SYMMETRY 11 1.5 LIE SYMMETRY OF THE ACOUSTIC EQUATION 13 1.6 LIE
ALGEBRA OF INFINITESIMAL OPERATORS FOR HOMOGENEOUS MEDIA 21 1.7
PARTICULAR CASES OF NON-HOMOGENEOUS MEDIA: LIE SYMMETRIES 24 1.7.1 MEDIA
WITH TRANSLATIONAL SYMMETRY 25 1.7.2 MEDIA WITH DILATATIONAL SYMMETRY 27
1.7.3 MEDIA WITH ROTATIONAL SYMMETRY 27 1.7.4 MEDIA WITH ROTATIONAL AND
DILATATIONAL SYMMETRY 28 1.7.5 MEDIA WITH SPIRAL SYMMETRY 29 2
SEPARATION OF VARIABLES. EXACT SOLUTIONS 31 2.1 GENERAL PRINCIPLES OF
THE SEPARATION OF VARIABLES IN LINEAR DIFFERENTIAL EQUATIONS 31 2.2
SEPARATION OF VARIABLES IN THE ACOUSTIC EQUATION FOR HOMOGENEOUS MEDIA
32 2.3 REVIEW OF DIFFERENT METHODS OF SEPARATION OF VARIABLES FOR
NON-HOMOGENEOUS MEDIA 38 2.4 NON-HOMOGENEOUS MEDIA WITH TRANSLATIONAL
SYMMETRY 39 2.5 NON-HOMOGENEOUS MEDIA WITH SPHERICAL SYMMETRY 41 2.6
NON-HOMOGENEOUS MEDIA WITH SPHERICAL AND DILATATIONAL SYMMETRY 44 2.7
NON-HOMOGENEOUS MEDIA WITH CYLINDRICAL SYMMETRY 47 2.8 USE OF GROUP
PROPERTIES OF ACOUSTIC EQUATIONS TO PRODUCE NEW SOLUTIONS FOR
HOMOGENEOUS MEDIA 51 2.9 USE OF GROUP PROPERTIES OF ACOUSTIC EQUATIONS
TO PRODUCE NEW SOLUTIONS FOR NON-HOMOGENEOUS MEDIA 62 3 SHORT WAVE
APPROXIMATION 71 3.1 DIMENSIONLESS FORM OF THE MAIN EQUATION 71 3.2
STRUCTURE OF OUTER ASYMPTOTIC EXPANSION 72 3.3 ACOUSTIC TRAJECTORIES ARE
CHARACTERISTIC OF PHASE ACOUSTIC EQUATIONS 76 3.4 TRAJECTORY
CALCULATIONS OF PRE-EXPONENTIAL FACTORS 78 3.5 LIE SYMMETRY OF THE PHASE
EQUATION 79 3.6 CONTACT SYMMETRY OF THE PHASE EQUATION 91 VI CONTENTS
3.7 SEPARATION OF VARIABLES. CONSTRUCTION OF SHORT WAVE ASYMPTOTICAL
SOLUTIONS 99 3.7.1 CARTESIAN COORDINATES 99 3.7.2 CYLINDRICAL
COORDINATES 103 3.7.3 SPHERICAL COORDINATES 107 3.8 ANALYSIS OF A
PARTICULAR CASE 111 4 MOMENTUM REPRESENTATION IN ACOUSTICS 117 4.1
INTEGRAL TRANSFORMATION OF THE MAIN EQUATION 117 4.2 MOMENTUM
REPRESENTATION OF THE ACOUSTIC EQUATION FOR NON-HOMOGENEOUS MEDIA OF A
PARTICULAR TYPE 118 4.2.1 MEDIA OF LINEAR TYPE 118 4.2.2 MEDIA OF
QUADRATIC TYPE 120 4.3 LIE SYMMETRY OF THE ACOUSTIC EQUATION FOR LINEAR
MEDIA 121 4.4 OPERATOR SYMMETRY OF THE ACOUSTIC EQUATION FOR LINEAR
MEDIA 124 4.5 ANALYSIS OF A PARTICULAR CASE OF LINEAR MEDIA 125 4.6
OPERATOR SYMMETRY OF THE ACOUSTIC EQUATION FOR QUADRATIC MEDIA 132 4.7
LIE SYMMETRY OF THE ACOUSTIC EQUATION FOR QUADRATIC MEDIA 137 4.8 LIE
SYMMETRY OF THE ACOUSTIC EQUATION FOR HOMOGENEOUS MEDIA 139 4.9
DISCUSSION ON THE MOMENTUM REPRESENTATION 144 REFERENCES 147 INDEX 149
|
| any_adam_object | 1 |
| author | Poluyanov, Leonid V. Aguilar, Antonio González, Miguel |
| author_GND | (DE-588)12778019X |
| author_facet | Poluyanov, Leonid V. Aguilar, Antonio González, Miguel |
| author_role | aut aut aut |
| author_sort | Poluyanov, Leonid V. |
| author_variant | l v p lv lvp a a aa m g mg |
| building | Verbundindex |
| bvnumber | BV010894355 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 6200 |
| classification_tum | PHY 252f |
| ctrlnum | (OCoLC)32894591 (DE-599)BVBBV010894355 |
| dewey-full | 534/.2/01515354 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 534 - Sound and related vibrations |
| dewey-raw | 534/.2/01515354 |
| dewey-search | 534/.2/01515354 |
| dewey-sort | 3534 12 71515354 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV010894355 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:00:42Z |
| institution | BVB |
| isbn | 0748402802 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007285559 |
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| physical | XIV, 151 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Taylor & Francis |
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| spelling | Poluyanov, Leonid V. Verfasser aut Group properties of the acoustic differential equation Leonid V. Poluyanov, Antonio Aguilar and Miguel González London [u.a.] Taylor & Francis 1995 XIV, 151 S. txt rdacontent n rdamedia nc rdacarrier Lie, Algèbres de ram Lie, Groupes de ram Ondes sonores ram Ondes élastiques ram Représentations de groupes ram Équations différentielles linéaires ram Mathematisches Modell Acoustical engineering Mathematical models Differential equations, Linear Elastic waves Lie algebras Lie groups Representations of groups Sound-waves Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Schallwelle (DE-588)4191490-9 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Schallwelle (DE-588)4191490-9 s Wellengleichung (DE-588)4065315-8 s Lie-Algebra (DE-588)4130355-6 s DE-604 Aguilar, Antonio Verfasser aut González, Miguel Verfasser (DE-588)12778019X aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007285559&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Poluyanov, Leonid V. Aguilar, Antonio González, Miguel Group properties of the acoustic differential equation Lie, Algèbres de ram Lie, Groupes de ram Ondes sonores ram Ondes élastiques ram Représentations de groupes ram Équations différentielles linéaires ram Mathematisches Modell Acoustical engineering Mathematical models Differential equations, Linear Elastic waves Lie algebras Lie groups Representations of groups Sound-waves Lie-Algebra (DE-588)4130355-6 gnd Schallwelle (DE-588)4191490-9 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4191490-9 (DE-588)4065315-8 |
| title | Group properties of the acoustic differential equation |
| title_auth | Group properties of the acoustic differential equation |
| title_exact_search | Group properties of the acoustic differential equation |
| title_full | Group properties of the acoustic differential equation Leonid V. Poluyanov, Antonio Aguilar and Miguel González |
| title_fullStr | Group properties of the acoustic differential equation Leonid V. Poluyanov, Antonio Aguilar and Miguel González |
| title_full_unstemmed | Group properties of the acoustic differential equation Leonid V. Poluyanov, Antonio Aguilar and Miguel González |
| title_short | Group properties of the acoustic differential equation |
| title_sort | group properties of the acoustic differential equation |
| topic | Lie, Algèbres de ram Lie, Groupes de ram Ondes sonores ram Ondes élastiques ram Représentations de groupes ram Équations différentielles linéaires ram Mathematisches Modell Acoustical engineering Mathematical models Differential equations, Linear Elastic waves Lie algebras Lie groups Representations of groups Sound-waves Lie-Algebra (DE-588)4130355-6 gnd Schallwelle (DE-588)4191490-9 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Lie, Algèbres de Lie, Groupes de Ondes sonores Ondes élastiques Représentations de groupes Équations différentielles linéaires Mathematisches Modell Acoustical engineering Mathematical models Differential equations, Linear Elastic waves Lie algebras Lie groups Representations of groups Sound-waves Lie-Algebra Schallwelle Wellengleichung |
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