Nonlinear periodic waves and their modulations: an introductory course
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2000
|
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions |
| Beschreibung: | xiv, 383 p. ill |
| ISBN: | 9789812792259 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV044635456 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 171120s2000 |||| o||u| ||||||eng d | ||
| 020 | |a 9789812792259 |9 978-981-279-225-9 | ||
| 024 | 7 | |a 10.1142/4513 |2 doi | |
| 035 | |a (ZDB-124-WOP)00004393 | ||
| 035 | |a (OCoLC)1012646020 | ||
| 035 | |a (DE-599)BVBBV044635456 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-92 | ||
| 082 | 0 | |a 530.14 |2 22 | |
| 100 | 1 | |a Kamchatnov, A. M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear periodic waves and their modulations |b an introductory course |c A.M. Kamchatnov |
| 264 | 1 | |a Singapore |b World Scientific Pub. Co. |c c2000 | |
| 300 | |a xiv, 383 p. |b ill | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 520 | |a Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions | ||
| 650 | 4 | |a Nonlinear waves | |
| 650 | 4 | |a Wave-motion, Theory of | |
| 650 | 4 | |a Solitons | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9789810244071 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 981024407X |
| 856 | 4 | 0 | |u http://www.worldscientific.com/worldscibooks/10.1142/4513#t=toc |x Verlag |z URL des Erstveroeffentlichers |3 Volltext |
| 912 | |a ZDB-124-WOP | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-030033428 | ||
| 966 | e | |u http://www.worldscientific.com/worldscibooks/10.1142/4513#t=toc |l FHN01 |p ZDB-124-WOP |q FHN_PDA_WOP |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804178048537329664 |
|---|---|
| any_adam_object | |
| author | Kamchatnov, A. M. |
| author_facet | Kamchatnov, A. M. |
| author_role | aut |
| author_sort | Kamchatnov, A. M. |
| author_variant | a m k am amk |
| building | Verbundindex |
| bvnumber | BV044635456 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00004393 (OCoLC)1012646020 (DE-599)BVBBV044635456 |
| dewey-full | 530.14 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14 |
| dewey-search | 530.14 |
| dewey-sort | 3530.14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03025nmm a2200397zc 4500</leader><controlfield tag="001">BV044635456</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">171120s2000 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812792259</subfield><subfield code="9">978-981-279-225-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1142/4513</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-124-WOP)00004393</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1012646020</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044635456</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.14</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kamchatnov, A. M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear periodic waves and their modulations</subfield><subfield code="b">an introductory course</subfield><subfield code="c">A.M. Kamchatnov</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore</subfield><subfield code="b">World Scientific Pub. Co.</subfield><subfield code="c">c2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiv, 383 p.</subfield><subfield code="b">ill</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear waves</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Wave-motion, Theory of</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Solitons</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9789810244071</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">981024407X</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/4513#t=toc</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveroeffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-124-WOP</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030033428</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/4513#t=toc</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-124-WOP</subfield><subfield code="q">FHN_PDA_WOP</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV044635456 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:47Z |
| institution | BVB |
| isbn | 9789812792259 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030033428 |
| oclc_num | 1012646020 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xiv, 383 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Kamchatnov, A. M. Verfasser aut Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov Singapore World Scientific Pub. Co. c2000 xiv, 383 p. ill txt rdacontent c rdamedia cr rdacarrier Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions Nonlinear waves Wave-motion, Theory of Solitons Erscheint auch als Druck-Ausgabe 9789810244071 Erscheint auch als Druck-Ausgabe 981024407X http://www.worldscientific.com/worldscibooks/10.1142/4513#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Kamchatnov, A. M. Nonlinear periodic waves and their modulations an introductory course Nonlinear waves Wave-motion, Theory of Solitons |
| title | Nonlinear periodic waves and their modulations an introductory course |
| title_auth | Nonlinear periodic waves and their modulations an introductory course |
| title_exact_search | Nonlinear periodic waves and their modulations an introductory course |
| title_full | Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov |
| title_fullStr | Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov |
| title_full_unstemmed | Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov |
| title_short | Nonlinear periodic waves and their modulations |
| title_sort | nonlinear periodic waves and their modulations an introductory course |
| title_sub | an introductory course |
| topic | Nonlinear waves Wave-motion, Theory of Solitons |
| topic_facet | Nonlinear waves Wave-motion, Theory of Solitons |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4513#t=toc |
| work_keys_str_mv | AT kamchatnovam nonlinearperiodicwavesandtheirmodulationsanintroductorycourse |