Title Solitons / P.G. Drazin

Published Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1983

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Description 1 online resource (viii, 136 pages) : illustrations Series London Mathematical Society lecture note series ; 85 London Mathematical Society lecture note series ; 85. 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 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 Bibliography Includes bibliographical references (pages 128-132) Notes Includes indexes Print version record Subject Solitons. SCIENCE -- Waves & Wave Mechanics. Solitons Soliton Solitons. Mathematische fysica. Solitons. Form Electronic book ISBN 9781107361010 110736101X 9780511662843 051166284X

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