Nonlinear waves: a geometrical approach
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
2018
|
| Series: | Series on analysis, applications, and computation
volume 9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xi, 196 Seiten Illustrationen |
| ISBN: | 9789813271609 |
Staff View
MARC
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| 245 | 1 | 0 | |a Nonlinear waves |b a geometrical approach |c by Petar Popivanov (Bulgarian Academy of Sciences, Bulgaria), Angela Slavova (Bulgarian Academy of Sciences, Bulgaria) |
| 264 | 1 | |a New Jersey |b World Scientific |c 2018 | |
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| 490 | 1 | |a Series on analysis, applications, and computation |v volume 9 | |
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| 650 | 4 | |a Nonlinear waves | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Nonlinear partial differential operators | |
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Record in the Search Index
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| adam_text | Contents Preface v 1. Introduction 1 1.1 1.2 1 1.3 1.4 1.5 2. 5 9 13 16 Traveling waves and their profiles 21 2.1 2.2 21 2.3 2.4 2.5 3. Introduction.......................................................................... Hodograph transformation and canonical forms of linear hyperbolic PDE in R2......................................................... Exercises on nonlinear systemsof PDE............................... Linear Volterra equations and evolution PDEs.................. Concluding remarks ............................................................ Introduction........................................................................... Preliminary notes on the traveling wave solutions of the Fornberg-Whitham equation................................................ Investigation of the case (Al)............................................. Investigation of the case (A2)............................................. Traveling wave solutions of the Vakhnenko equation. Geometrical interpretation................................................... Explicit formulas to the solutions of several equations of physics and geometry 3.1 3.2 3.3 Introduction........................................................................... Special solutions of semilinear К-G type equations in the multidimensional case ......................................................... К-P equation and X, Y shallowwater waves in the oceans ІХ 22 24 25 31 37 37 38 41
Nonlinear Waves: A Geometrical Approach x 3.4 3.5 3.6 4. 55 4.1 4.2 55 4.4 4.5 4.6 Introduction........................................................................... Interaction of 2 peakon solutions of the Camassa-Holm equation................................................................................. First integrals of the dynamical system corresponding to the ծ-evolution equation...................................................... First integrals of the ODE system corresponding to the Ansatz Eq. (4.3) solutions of the generalized CamassaHolm Eq. (4.1) ..................................................................... Interaction of kink-peakon solutions to the generalized Camassa-Holm equation. First integral.............................. Concluding remarks ............................................................ Introduction to the dressing method and application to the cubic NLS 5.1 5.2 5.3 5.4 5.5 5.6 6. 44 48 49 First integrals of systems of ODE having jumpdiscontinuities 4.3 5. Solutions of first order linear and cubic nonlinear first order hyperbolic pseudodifferential equations.............................. Possible generalizations of Proposition 3.3........................ Exact solutions of Tzitzeica equation................................. Introduction........................................................................... Preliminary notes.................................................................. Dressing method and Riemann-Hilbert problem. Short survey...........................................................................
Geometrical interpretation of the soliton solutions............ Concluding remarks ............................................................ Appendix. Volterra integral equations in infiniteintervals Direct methods in soliton theory. Hirota’s approach 6.1 6.2 6.3 6.4 6.5 56 60 63 66 69 71 71 72 74 84 89 90 97 Simplified Hirota’s method in soliton theory..................... 97 Short description of direct Hirota’s approach for finding soliton solutions of some classes of nonlinear PDEs .... 106 Bilinear equations of the type L(DX, = 0............... 110 Interaction of 3 waves to Kadomtsev-Petviashvili equation and of two loop solutions of the Vakhnenko equation ... 113 Appendix. Sin-Gordon equation. Fluxons and their interaction.............................................................................. 116
Contents 6.5.1 7. 121 Special type solutions of several evolution PDEs 123 7.1 7.2 123 7.3 7.4 8. Rational solutions of some equations of mathematical physics............................................. xi Introduction.......................................................................... Traveling waves. Method of the auxiliary solution (of the simplest equation) ............................................................... Traveling waves for some generalized Boussinesq type equations .............................................................................. 7.3.1 Construction of traveling wave solutions to Boussinesq type PDE............................................. Interaction of two solitons and rogue waves..................... 124 142 143 148 Regularity properties of several hyperbolic equations and systems 155 8.1 8.2 8.3 8.4 8.5 Introduction........................................................................... Regularity results on the 2D semilinear wave equation having radially smooth Cauchy data................................. Wave fronts of the solutions of fully nonlinear symmetric positive systems of PDE...................................................... 8.3.1 Formulation of the main results ........................... 8.3.2 Proof of Theorem 8.4............................................. Regularizing property of the solutions of adissipative semilinear wave equation...................................................... Formulation and investigation of the maindissipative nonlinear wave
equation...................................................... 155 156 165 166 172 176 177 Bibliography 187 Index 195
|
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| author | Popivanov, Petăr R. 1946- Slavova, Angela |
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| discipline | Physik Mathematik |
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| id | DE-604.BV045491493 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:19:32Z |
| institution | BVB |
| isbn | 9789813271609 |
| language | English |
| lccn | 018043691 |
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| owner_facet | DE-739 DE-91G DE-BY-TUM |
| physical | xi, 196 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on analysis, applications, and computation |
| series2 | Series on analysis, applications, and computation |
| spelling | Popivanov, Petăr R. 1946- Verfasser (DE-588)1026818737 aut Nonlinear waves a geometrical approach by Petar Popivanov (Bulgarian Academy of Sciences, Bulgaria), Angela Slavova (Bulgarian Academy of Sciences, Bulgaria) New Jersey World Scientific 2018 xi, 196 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Series on analysis, applications, and computation volume 9 Includes bibliographical references and index Nonlinear wave equations Nonlinear waves Mathematical physics Nonlinear partial differential operators Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 s Mathematische Physik (DE-588)4037952-8 s DE-604 Slavova, Angela Verfasser aut Series on analysis, applications, and computation volume 9 (DE-604)BV025564855 9 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030876353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Popivanov, Petăr R. 1946- Slavova, Angela Nonlinear waves a geometrical approach Series on analysis, applications, and computation Nonlinear wave equations Nonlinear waves Mathematical physics Nonlinear partial differential operators Nichtlineare Welle (DE-588)4042102-8 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4042102-8 (DE-588)4037952-8 |
| title | Nonlinear waves a geometrical approach |
| title_auth | Nonlinear waves a geometrical approach |
| title_exact_search | Nonlinear waves a geometrical approach |
| title_full | Nonlinear waves a geometrical approach by Petar Popivanov (Bulgarian Academy of Sciences, Bulgaria), Angela Slavova (Bulgarian Academy of Sciences, Bulgaria) |
| title_fullStr | Nonlinear waves a geometrical approach by Petar Popivanov (Bulgarian Academy of Sciences, Bulgaria), Angela Slavova (Bulgarian Academy of Sciences, Bulgaria) |
| title_full_unstemmed | Nonlinear waves a geometrical approach by Petar Popivanov (Bulgarian Academy of Sciences, Bulgaria), Angela Slavova (Bulgarian Academy of Sciences, Bulgaria) |
| title_short | Nonlinear waves |
| title_sort | nonlinear waves a geometrical approach |
| title_sub | a geometrical approach |
| topic | Nonlinear wave equations Nonlinear waves Mathematical physics Nonlinear partial differential operators Nichtlineare Welle (DE-588)4042102-8 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Nonlinear wave equations Nonlinear waves Mathematical physics Nonlinear partial differential operators Nichtlineare Welle Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030876353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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