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Solitons /:

A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory...

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Bibliographic Details
Main Author:	Drazin, P. G.
Format:	Electronic eBook
Language:	English
Published:	Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1983.
Series:	London Mathematical Society lecture note series ; 85.
Subjects:	Solitons. SCIENCE > Waves & Wave Mechanics. Solitons Soliton Mathematische fysica.
Online Access:	DE-862 DE-863
Summary:	A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering.
Item Description:	Includes indexes.
Physical Description:	1 online resource (viii, 136 pages) : illustrations
Bibliography:	Includes bibliographical references (pages 128-132).
ISBN:	9781107361010 110736101X 9780511662843 051166284X

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520			\|a A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering.
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contents	Cover; Title; Copyright; Contents; Preface; Chapter 1 TEE KORTEWEG-DE VRIES EQUATION; 1. The discovery of solitary waves; 2. Fundamental ideas; 3. The discovery of soliton interactions; 4. Applications of the KdV equation; Problems; CHAPTER 2 CNOIDAL WAVES; 1. Wave solutions of the KdV solution; 2. Solitary waves; 3. General waves of permanent form; 4. Description of waves in terms of elliptic functions; 5. Infinitesimal waves; 6. Solitary waves again; Problems; Chapter 3 CONSERVATION LAWS; 1. Fundamental ideas; 2. Gardner's transformation; Problems Chapter 4 THE INITIAL-VALUE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION1. The problem; 2. Sketch of the method of inverse scattering; 3. The scattering problem; 4. The evolution equation; 5. Solution of the scattering problem for t> 0; 6. The inverse scattering problem; 7. Qualitative character of the solution; 8. Example: the delta-function potential; 9. Example: g(x) = -- 2sech2x; 10. Example: g(x) = -- 6sech2x; 11. Examples: sech-squared potentials; 12. Examples: some numerical results; 13. Reflectionless potentials; Chapter 5 THE LAX METHOD 1. Description of the method in terms of operatorsProblems; Chapter 6 THE SINE-GORDON EQUATION; 1. Introduction; 2. Waves and solitons; 3. Some other simple explicit solutions; 4. The interaction of two solitons; 5. A breather; 6. The method of inverse scattering; Problems; Chapter 7 BACKLUND TRANSFORMATIONS; 1. Introduction; 2. The sine-Gordon equation; 3. The KdV equation; Problems; 1. Epilogue; Appendix A DERIVATION OF THE INTEGRAL EQUATION FOR INVERSE SCATTERING; Bibliography and author index; Motion picture index; Subject index
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series	London Mathematical Society lecture note series ;
series2	London Mathematical Society lecture note series ;
spelling	Drazin, P. G. Solitons / P.G. Drazin. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1983. 1 online resource (viii, 136 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 85 Includes bibliographical references (pages 128-132). Includes indexes. Print version record. A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering. Cover; Title; Copyright; Contents; Preface; Chapter 1 TEE KORTEWEG-DE VRIES EQUATION; 1. The discovery of solitary waves; 2. Fundamental ideas; 3. The discovery of soliton interactions; 4. Applications of the KdV equation; Problems; CHAPTER 2 CNOIDAL WAVES; 1. Wave solutions of the KdV solution; 2. Solitary waves; 3. General waves of permanent form; 4. Description of waves in terms of elliptic functions; 5. Infinitesimal waves; 6. Solitary waves again; Problems; Chapter 3 CONSERVATION LAWS; 1. Fundamental ideas; 2. Gardner's transformation; Problems Chapter 4 THE INITIAL-VALUE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION1. The problem; 2. Sketch of the method of inverse scattering; 3. The scattering problem; 4. The evolution equation; 5. Solution of the scattering problem for t> 0; 6. The inverse scattering problem; 7. Qualitative character of the solution; 8. Example: the delta-function potential; 9. Example: g(x) = -- 2sech2x; 10. Example: g(x) = -- 6sech2x; 11. Examples: sech-squared potentials; 12. Examples: some numerical results; 13. Reflectionless potentials; Chapter 5 THE LAX METHOD 1. Description of the method in terms of operatorsProblems; Chapter 6 THE SINE-GORDON EQUATION; 1. Introduction; 2. Waves and solitons; 3. Some other simple explicit solutions; 4. The interaction of two solitons; 5. A breather; 6. The method of inverse scattering; Problems; Chapter 7 BACKLUND TRANSFORMATIONS; 1. Introduction; 2. The sine-Gordon equation; 3. The KdV equation; Problems; 1. Epilogue; Appendix A DERIVATION OF THE INTEGRAL EQUATION FOR INVERSE SCATTERING; Bibliography and author index; Motion picture index; Subject index Solitons. http://id.loc.gov/authorities/subjects/sh85124672 Solitons. SCIENCE Waves & Wave Mechanics. bisacsh Solitons fast Soliton gnd http://d-nb.info/gnd/4135213-0 Solitons. gtt Mathematische fysica. gtt Solitons. ram Print version: Drazin, P.G. Solitons. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1983 0521274222 (DLC) 83007170 (OCoLC)9442461 London Mathematical Society lecture note series ; 85. http://id.loc.gov/authorities/names/n42015587
spellingShingle	Drazin, P. G. Solitons / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; Chapter 1 TEE KORTEWEG-DE VRIES EQUATION; 1. The discovery of solitary waves; 2. Fundamental ideas; 3. The discovery of soliton interactions; 4. Applications of the KdV equation; Problems; CHAPTER 2 CNOIDAL WAVES; 1. Wave solutions of the KdV solution; 2. Solitary waves; 3. General waves of permanent form; 4. Description of waves in terms of elliptic functions; 5. Infinitesimal waves; 6. Solitary waves again; Problems; Chapter 3 CONSERVATION LAWS; 1. Fundamental ideas; 2. Gardner's transformation; Problems Chapter 4 THE INITIAL-VALUE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION1. The problem; 2. Sketch of the method of inverse scattering; 3. The scattering problem; 4. The evolution equation; 5. Solution of the scattering problem for t> 0; 6. The inverse scattering problem; 7. Qualitative character of the solution; 8. Example: the delta-function potential; 9. Example: g(x) = -- 2sech2x; 10. Example: g(x) = -- 6sech2x; 11. Examples: sech-squared potentials; 12. Examples: some numerical results; 13. Reflectionless potentials; Chapter 5 THE LAX METHOD 1. Description of the method in terms of operatorsProblems; Chapter 6 THE SINE-GORDON EQUATION; 1. Introduction; 2. Waves and solitons; 3. Some other simple explicit solutions; 4. The interaction of two solitons; 5. A breather; 6. The method of inverse scattering; Problems; Chapter 7 BACKLUND TRANSFORMATIONS; 1. Introduction; 2. The sine-Gordon equation; 3. The KdV equation; Problems; 1. Epilogue; Appendix A DERIVATION OF THE INTEGRAL EQUATION FOR INVERSE SCATTERING; Bibliography and author index; Motion picture index; Subject index Solitons. http://id.loc.gov/authorities/subjects/sh85124672 Solitons. SCIENCE Waves & Wave Mechanics. bisacsh Solitons fast Soliton gnd http://d-nb.info/gnd/4135213-0 Solitons. gtt Mathematische fysica. gtt Solitons. ram
subject_GND	http://id.loc.gov/authorities/subjects/sh85124672 http://d-nb.info/gnd/4135213-0
title	Solitons /
title_auth	Solitons /
title_exact_search	Solitons /
title_full	Solitons / P.G. Drazin.
title_fullStr	Solitons / P.G. Drazin.
title_full_unstemmed	Solitons / P.G. Drazin.
title_short	Solitons /
title_sort	solitons
topic	Solitons. http://id.loc.gov/authorities/subjects/sh85124672 Solitons. SCIENCE Waves & Wave Mechanics. bisacsh Solitons fast Soliton gnd http://d-nb.info/gnd/4135213-0 Solitons. gtt Mathematische fysica. gtt Solitons. ram
topic_facet	Solitons. SCIENCE Waves & Wave Mechanics. Solitons Soliton Mathematische fysica.
work_keys_str_mv	AT drazinpg solitons

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