Bäcklund transformations and their applications /:
Ba?cklund transformations and their applications.
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| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York :
Academic Press,
1982.
|
| Series: | Mathematics in science and engineering ;
v. 161. |
| Subjects: | |
| Online Access: | DE-862 DE-863 DE-862 DE-863 |
| Summary: | Ba?cklund transformations and their applications. |
| Physical Description: | 1 online resource (xiii, 334 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 302-321) and indexes. |
| ISBN: | 9780125928502 0125928505 9780080956671 008095667X 1282288822 9781282288829 9786612288821 6612288825 |
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| 245 | 1 | 0 | |a Bäcklund transformations and their applications / |c C. Rogers and W.F. Shadwick. |
| 260 | |a New York : |b Academic Press, |c 1982. | ||
| 300 | |a 1 online resource (xiii, 334 pages) : |b illustrations | ||
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 161 | |
| 504 | |a Includes bibliographical references (pages 302-321) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Ba?cklund transformations and their applications. | ||
| 505 | 0 | |a Front Cover; Bäcklund Transformations and Their Applications; Copyright Page; Contents; Preface; Acknowledgments; General Introduction and Outline; CHAPTER 1. Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics; 1.1 The Origin and Importance of Bäcklund Transformations; 1.2 The 1 + 1 Sine-Gordon Equation. The Permutability Theorem. Bianchi Diagrams; 1.3 Ultrashort Optical Pulse Propagation in a Resonant Medium. 2Np Light Pulses | |
| 505 | 8 | |a 1.4 Propagation of Magnetic Flux through a Long Josephson Junction. An Elliptic Analog of the 1 + 1 Sine-Gordon Equation. Generation of Solutions via a Bäcklund Transformation1.5 The Cole-Hopf Reduction of Burgers' Equation to the Heat Equation. Solution of Initial Value Problems; 1.6 Finite Amplitude Dispersive Waves and the Korteweg-deVries Equation; 1.7 The Wahlquist-Estabrook Invariant Transformation of the Korteweg-deVries Equation. The Soliton Ladder; 1.8 An Auto-Bäcklund Transformation of the Modified Korteweg-deVries Equation. The Permutability Theorem and Generation of Solutions | |
| 505 | 8 | |a 1.9 The Miura Transformation1.10 A Nonlinear Schrödinger Equation; 1.11 Bäcklund Transformations and the AKNS System. An Invariant Transformation of the Cubic Schrödinger Equation; 1.12 The Hirota Bilinear Operator Formulation of Bäcklund Transformations. The Boussinesq Equation. Kaup's Higher Order Water Wave Equation; 1.13 Bäcklund Transformations for Higher Order Korteweg-deVries Equations; 1.14 Bäcklund Transformations in Higher Dimensions. The Sine-Gordon Equation in 3 + 1 Dimensions. The Kadomtsev-Petviashvili Equation. The Yang Equations | |
| 505 | 8 | |a 1.15 The Benjamin-Ono Equation for Internal Deep Water Waves. The Nakamura Transformation1.16 A Bäcklund Transformation for Joseph's Equation for Internal Waves in a Stratified Fluid with Finite Depth; 1.17 Bäcklund Transformations of Nonlinear Lattice Equations in Their Continuum Approximation. The Konno-Sanuki Transformation; 1.18 Bäcklund Transformations of Nonlinear Differential-Difference Equations. The Toda and Associated Lattices; 1.19 Bäcklund Transformations in General Relativity. The Ernst Equations. Neugebauer's Permutability Theorem | |
| 505 | 8 | |a CHAPTER 2. A Local Jet-Bundle Formulation of Bäcklund Transformations2.1 Preliminaries; 2.2 Contact Structures; 2.3 Partial Differential Equations on Jet Bundles; 2.4 Fibered Products of Jet Bundles; 2.5 Bäcklund Maps; 2.6 Bäcklund Transformations Determined by Bäcklund Maps; 2.7 Symmetries of Differential Equations and One-Parameter Families of Bäcklund Maps; 2.8 The Wahlquist-Estabrook Procedure; CHAPTER 3. Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics; 3.1 The Reciprocal Relations and the Haar Transformation | |
| 546 | |a English. | ||
| 650 | 0 | |a Differential equations, Partial. |0 http://id.loc.gov/authorities/subjects/sh85037912 | |
| 650 | 0 | |a Bäcklund transformations. |0 http://id.loc.gov/authorities/subjects/sh85010800 | |
| 650 | 0 | |a Jet bundles (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85070153 | |
| 650 | 0 | |a Mathematical physics. |0 http://id.loc.gov/authorities/subjects/sh85082129 | |
| 650 | 6 | |a Transformations de Bäcklund. | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
| 650 | 6 | |a Physique mathématique. | |
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| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
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| 650 | 7 | |a Differential equations, Partial |2 fast | |
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| 758 | |i has work: |a Bäcklund transformations and their applications (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH94qJrfJYwFDpbjHBXXBd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Rogers, C. |t Bäcklund transformations and their applications. |d New York : Academic Press, 1982 |z 9780125928502 |w (DLC) 81022783 |w (OCoLC)8051705 |
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Record in the Search Index
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| _version_ | 1829094640366649344 |
| adam_text | |
| any_adam_object | |
| author | Rogers, C. |
| author2 | Shadwick, W. F., 1951- |
| author2_role | |
| author2_variant | w f s wf wfs |
| author_GND | http://id.loc.gov/authorities/names/n81145178 http://id.loc.gov/authorities/names/n79086583 |
| author_facet | Rogers, C. Shadwick, W. F., 1951- |
| author_role | |
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| callnumber-first | Q - Science |
| callnumber-label | QA374 |
| callnumber-raw | QA374 .R64 1982eb |
| callnumber-search | QA374 .R64 1982eb |
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| callnumber-subject | QA - Mathematics |
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| contents | Front Cover; Bäcklund Transformations and Their Applications; Copyright Page; Contents; Preface; Acknowledgments; General Introduction and Outline; CHAPTER 1. Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics; 1.1 The Origin and Importance of Bäcklund Transformations; 1.2 The 1 + 1 Sine-Gordon Equation. The Permutability Theorem. Bianchi Diagrams; 1.3 Ultrashort Optical Pulse Propagation in a Resonant Medium. 2Np Light Pulses 1.4 Propagation of Magnetic Flux through a Long Josephson Junction. An Elliptic Analog of the 1 + 1 Sine-Gordon Equation. Generation of Solutions via a Bäcklund Transformation1.5 The Cole-Hopf Reduction of Burgers' Equation to the Heat Equation. Solution of Initial Value Problems; 1.6 Finite Amplitude Dispersive Waves and the Korteweg-deVries Equation; 1.7 The Wahlquist-Estabrook Invariant Transformation of the Korteweg-deVries Equation. The Soliton Ladder; 1.8 An Auto-Bäcklund Transformation of the Modified Korteweg-deVries Equation. The Permutability Theorem and Generation of Solutions 1.9 The Miura Transformation1.10 A Nonlinear Schrödinger Equation; 1.11 Bäcklund Transformations and the AKNS System. An Invariant Transformation of the Cubic Schrödinger Equation; 1.12 The Hirota Bilinear Operator Formulation of Bäcklund Transformations. The Boussinesq Equation. Kaup's Higher Order Water Wave Equation; 1.13 Bäcklund Transformations for Higher Order Korteweg-deVries Equations; 1.14 Bäcklund Transformations in Higher Dimensions. The Sine-Gordon Equation in 3 + 1 Dimensions. The Kadomtsev-Petviashvili Equation. The Yang Equations 1.15 The Benjamin-Ono Equation for Internal Deep Water Waves. The Nakamura Transformation1.16 A Bäcklund Transformation for Joseph's Equation for Internal Waves in a Stratified Fluid with Finite Depth; 1.17 Bäcklund Transformations of Nonlinear Lattice Equations in Their Continuum Approximation. The Konno-Sanuki Transformation; 1.18 Bäcklund Transformations of Nonlinear Differential-Difference Equations. The Toda and Associated Lattices; 1.19 Bäcklund Transformations in General Relativity. The Ernst Equations. Neugebauer's Permutability Theorem CHAPTER 2. A Local Jet-Bundle Formulation of Bäcklund Transformations2.1 Preliminaries; 2.2 Contact Structures; 2.3 Partial Differential Equations on Jet Bundles; 2.4 Fibered Products of Jet Bundles; 2.5 Bäcklund Maps; 2.6 Bäcklund Transformations Determined by Bäcklund Maps; 2.7 Symmetries of Differential Equations and One-Parameter Families of Bäcklund Maps; 2.8 The Wahlquist-Estabrook Procedure; CHAPTER 3. Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics; 3.1 The Reciprocal Relations and the Haar Transformation |
| ctrlnum | (OCoLC)316568332 |
| dewey-full | 515.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn316568332 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:36:20Z |
| institution | BVB |
| isbn | 9780125928502 0125928505 9780080956671 008095667X 1282288822 9781282288829 9786612288821 6612288825 |
| language | English |
| oclc_num | 316568332 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 334 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Academic Press, |
| record_format | marc |
| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Rogers, C. http://id.loc.gov/authorities/names/n81145178 Bäcklund transformations and their applications / C. Rogers and W.F. Shadwick. New York : Academic Press, 1982. 1 online resource (xiii, 334 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 161 Includes bibliographical references (pages 302-321) and indexes. Print version record. Ba?cklund transformations and their applications. Front Cover; Bäcklund Transformations and Their Applications; Copyright Page; Contents; Preface; Acknowledgments; General Introduction and Outline; CHAPTER 1. Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics; 1.1 The Origin and Importance of Bäcklund Transformations; 1.2 The 1 + 1 Sine-Gordon Equation. The Permutability Theorem. Bianchi Diagrams; 1.3 Ultrashort Optical Pulse Propagation in a Resonant Medium. 2Np Light Pulses 1.4 Propagation of Magnetic Flux through a Long Josephson Junction. An Elliptic Analog of the 1 + 1 Sine-Gordon Equation. Generation of Solutions via a Bäcklund Transformation1.5 The Cole-Hopf Reduction of Burgers' Equation to the Heat Equation. Solution of Initial Value Problems; 1.6 Finite Amplitude Dispersive Waves and the Korteweg-deVries Equation; 1.7 The Wahlquist-Estabrook Invariant Transformation of the Korteweg-deVries Equation. The Soliton Ladder; 1.8 An Auto-Bäcklund Transformation of the Modified Korteweg-deVries Equation. The Permutability Theorem and Generation of Solutions 1.9 The Miura Transformation1.10 A Nonlinear Schrödinger Equation; 1.11 Bäcklund Transformations and the AKNS System. An Invariant Transformation of the Cubic Schrödinger Equation; 1.12 The Hirota Bilinear Operator Formulation of Bäcklund Transformations. The Boussinesq Equation. Kaup's Higher Order Water Wave Equation; 1.13 Bäcklund Transformations for Higher Order Korteweg-deVries Equations; 1.14 Bäcklund Transformations in Higher Dimensions. The Sine-Gordon Equation in 3 + 1 Dimensions. The Kadomtsev-Petviashvili Equation. The Yang Equations 1.15 The Benjamin-Ono Equation for Internal Deep Water Waves. The Nakamura Transformation1.16 A Bäcklund Transformation for Joseph's Equation for Internal Waves in a Stratified Fluid with Finite Depth; 1.17 Bäcklund Transformations of Nonlinear Lattice Equations in Their Continuum Approximation. The Konno-Sanuki Transformation; 1.18 Bäcklund Transformations of Nonlinear Differential-Difference Equations. The Toda and Associated Lattices; 1.19 Bäcklund Transformations in General Relativity. The Ernst Equations. Neugebauer's Permutability Theorem CHAPTER 2. A Local Jet-Bundle Formulation of Bäcklund Transformations2.1 Preliminaries; 2.2 Contact Structures; 2.3 Partial Differential Equations on Jet Bundles; 2.4 Fibered Products of Jet Bundles; 2.5 Bäcklund Maps; 2.6 Bäcklund Transformations Determined by Bäcklund Maps; 2.7 Symmetries of Differential Equations and One-Parameter Families of Bäcklund Maps; 2.8 The Wahlquist-Estabrook Procedure; CHAPTER 3. Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics; 3.1 The Reciprocal Relations and the Haar Transformation English. Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Bäcklund transformations. http://id.loc.gov/authorities/subjects/sh85010800 Jet bundles (Mathematics) http://id.loc.gov/authorities/subjects/sh85070153 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Transformations de Bäcklund. Équations aux dérivées partielles. Physique mathématique. Fibrés des jets (Mathématiques) MATHEMATICS Differential Equations Partial. bisacsh Bäcklund transformations fast Differential equations, Partial fast Jet bundles (Mathematics) fast Mathematical physics fast Partiële differentiaalvergelijkingen. gtt Natuurkunde. gtt Toepassingen. gtt Bäcklund transformaties. gtt Shadwick, W. F., 1951- https://id.oclc.org/worldcat/entity/E39PCjHx7mgCMmJKBvM7ytkKJP http://id.loc.gov/authorities/names/n79086583 has work: Bäcklund transformations and their applications (Text) https://id.oclc.org/worldcat/entity/E39PCH94qJrfJYwFDpbjHBXXBd https://id.oclc.org/worldcat/ontology/hasWork Print version: Rogers, C. Bäcklund transformations and their applications. New York : Academic Press, 1982 9780125928502 (DLC) 81022783 (OCoLC)8051705 Mathematics in science and engineering ; v. 161. http://id.loc.gov/authorities/names/n42015986 |
| spellingShingle | Rogers, C. Bäcklund transformations and their applications / Mathematics in science and engineering ; Front Cover; Bäcklund Transformations and Their Applications; Copyright Page; Contents; Preface; Acknowledgments; General Introduction and Outline; CHAPTER 1. Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics; 1.1 The Origin and Importance of Bäcklund Transformations; 1.2 The 1 + 1 Sine-Gordon Equation. The Permutability Theorem. Bianchi Diagrams; 1.3 Ultrashort Optical Pulse Propagation in a Resonant Medium. 2Np Light Pulses 1.4 Propagation of Magnetic Flux through a Long Josephson Junction. An Elliptic Analog of the 1 + 1 Sine-Gordon Equation. Generation of Solutions via a Bäcklund Transformation1.5 The Cole-Hopf Reduction of Burgers' Equation to the Heat Equation. Solution of Initial Value Problems; 1.6 Finite Amplitude Dispersive Waves and the Korteweg-deVries Equation; 1.7 The Wahlquist-Estabrook Invariant Transformation of the Korteweg-deVries Equation. The Soliton Ladder; 1.8 An Auto-Bäcklund Transformation of the Modified Korteweg-deVries Equation. The Permutability Theorem and Generation of Solutions 1.9 The Miura Transformation1.10 A Nonlinear Schrödinger Equation; 1.11 Bäcklund Transformations and the AKNS System. An Invariant Transformation of the Cubic Schrödinger Equation; 1.12 The Hirota Bilinear Operator Formulation of Bäcklund Transformations. The Boussinesq Equation. Kaup's Higher Order Water Wave Equation; 1.13 Bäcklund Transformations for Higher Order Korteweg-deVries Equations; 1.14 Bäcklund Transformations in Higher Dimensions. The Sine-Gordon Equation in 3 + 1 Dimensions. The Kadomtsev-Petviashvili Equation. The Yang Equations 1.15 The Benjamin-Ono Equation for Internal Deep Water Waves. The Nakamura Transformation1.16 A Bäcklund Transformation for Joseph's Equation for Internal Waves in a Stratified Fluid with Finite Depth; 1.17 Bäcklund Transformations of Nonlinear Lattice Equations in Their Continuum Approximation. The Konno-Sanuki Transformation; 1.18 Bäcklund Transformations of Nonlinear Differential-Difference Equations. The Toda and Associated Lattices; 1.19 Bäcklund Transformations in General Relativity. The Ernst Equations. Neugebauer's Permutability Theorem CHAPTER 2. A Local Jet-Bundle Formulation of Bäcklund Transformations2.1 Preliminaries; 2.2 Contact Structures; 2.3 Partial Differential Equations on Jet Bundles; 2.4 Fibered Products of Jet Bundles; 2.5 Bäcklund Maps; 2.6 Bäcklund Transformations Determined by Bäcklund Maps; 2.7 Symmetries of Differential Equations and One-Parameter Families of Bäcklund Maps; 2.8 The Wahlquist-Estabrook Procedure; CHAPTER 3. Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics; 3.1 The Reciprocal Relations and the Haar Transformation Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Bäcklund transformations. http://id.loc.gov/authorities/subjects/sh85010800 Jet bundles (Mathematics) http://id.loc.gov/authorities/subjects/sh85070153 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Transformations de Bäcklund. Équations aux dérivées partielles. Physique mathématique. Fibrés des jets (Mathématiques) MATHEMATICS Differential Equations Partial. bisacsh Bäcklund transformations fast Differential equations, Partial fast Jet bundles (Mathematics) fast Mathematical physics fast Partiële differentiaalvergelijkingen. gtt Natuurkunde. gtt Toepassingen. gtt Bäcklund transformaties. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037912 http://id.loc.gov/authorities/subjects/sh85010800 http://id.loc.gov/authorities/subjects/sh85070153 http://id.loc.gov/authorities/subjects/sh85082129 |
| title | Bäcklund transformations and their applications / |
| title_auth | Bäcklund transformations and their applications / |
| title_exact_search | Bäcklund transformations and their applications / |
| title_full | Bäcklund transformations and their applications / C. Rogers and W.F. Shadwick. |
| title_fullStr | Bäcklund transformations and their applications / C. Rogers and W.F. Shadwick. |
| title_full_unstemmed | Bäcklund transformations and their applications / C. Rogers and W.F. Shadwick. |
| title_short | Bäcklund transformations and their applications / |
| title_sort | backlund transformations and their applications |
| topic | Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Bäcklund transformations. http://id.loc.gov/authorities/subjects/sh85010800 Jet bundles (Mathematics) http://id.loc.gov/authorities/subjects/sh85070153 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Transformations de Bäcklund. Équations aux dérivées partielles. Physique mathématique. Fibrés des jets (Mathématiques) MATHEMATICS Differential Equations Partial. bisacsh Bäcklund transformations fast Differential equations, Partial fast Jet bundles (Mathematics) fast Mathematical physics fast Partiële differentiaalvergelijkingen. gtt Natuurkunde. gtt Toepassingen. gtt Bäcklund transformaties. gtt |
| topic_facet | Differential equations, Partial. Bäcklund transformations. Jet bundles (Mathematics) Mathematical physics. Transformations de Bäcklund. Équations aux dérivées partielles. Physique mathématique. Fibrés des jets (Mathématiques) MATHEMATICS Differential Equations Partial. Bäcklund transformations Differential equations, Partial Mathematical physics Partiële differentiaalvergelijkingen. Natuurkunde. Toepassingen. Bäcklund transformaties. |
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