Ebook: Solitons in Physics, Mathematics, and Nonlinear Optics

This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshops focussed on the main parts of the theory of solitons and on the applications of solitons in physics, biology and engineering, with a special concentration on nonlinear optics. We thank the Coordinating Committee: James Glimm, Daniel Joseph, Barbara Keyfitz, An­ Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for drew planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers for Solitons in Physics and Mathematics, Alan Newell, Peter Olver, and David Sattinger, and for Nonlinear Optics and Plasma Physics, David Kaup and Yuji Kodama for their efforts in bringing together many of the major figures in those research fields in which solitons in physics, mathematics, and nonlinear optics theories are used. A vner Friedman Willard Miller, Jr. PREFACE This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 LM. A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry.

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This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 IMA year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry. The present contributions represent only a fraction of these areas, but give the reader a good overview of several current research directions, including optics, fluid dynamics, inverse scattering, cellular automata, B?cklund equations, symmetries and Hamiltonian systems.

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This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 IMA year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry. The present contributions represent only a fraction of these areas, but give the reader a good overview of several current research directions, including optics, fluid dynamics, inverse scattering, cellular automata, B?cklund equations, symmetries and Hamiltonian systems.
Content:
Front Matter....Pages i-xiii
Nonlinear Evolution Equations, Inverse Scattering and Cellular Automata....Pages 1-26
Painlev? Equations and the Inverse Scattering and Inverse Monodromy Transforms....Pages 27-43
Chaotic Behavior in Nonlinear Polarization Dynamics....Pages 45-63
New Manifestations of Solitons....Pages 65-77
A Unified Approach to Recursion Operators....Pages 79-96
Isospectral Flows: Their Hamiltonian Structures, Miura Maps and Master Symmetries....Pages 97-121
Integrable Nonlinear Evolution Equations in the Description of Waves in the Shallow-Water Long-Wave Approximation....Pages 123-153
Transient Solitons in Stimulated Raman Scattering....Pages 155-163
Monodromy Preserving Deformation of Linear Ordinary and Partial Differential Equations....Pages 165-174
B?cklund Transformations and the Painlev? Property....Pages 175-202
Symmetry Groups of Multidimensional Integrable Nonlinear Systems....Pages 203-215

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This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 IMA year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry. The present contributions represent only a fraction of these areas, but give the reader a good overview of several current research directions, including optics, fluid dynamics, inverse scattering, cellular automata, B?cklund equations, symmetries and Hamiltonian systems.
Content:
Front Matter....Pages i-xiii
Nonlinear Evolution Equations, Inverse Scattering and Cellular Automata....Pages 1-26
Painlev? Equations and the Inverse Scattering and Inverse Monodromy Transforms....Pages 27-43
Chaotic Behavior in Nonlinear Polarization Dynamics....Pages 45-63
New Manifestations of Solitons....Pages 65-77
A Unified Approach to Recursion Operators....Pages 79-96
Isospectral Flows: Their Hamiltonian Structures, Miura Maps and Master Symmetries....Pages 97-121
Integrable Nonlinear Evolution Equations in the Description of Waves in the Shallow-Water Long-Wave Approximation....Pages 123-153
Transient Solitons in Stimulated Raman Scattering....Pages 155-163
Monodromy Preserving Deformation of Linear Ordinary and Partial Differential Equations....Pages 165-174
B?cklund Transformations and the Painlev? Property....Pages 175-202
Symmetry Groups of Multidimensional Integrable Nonlinear Systems....Pages 203-215
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