Ebook: Nonlinear Phenomena in Physics and Biology

The Advanced Study Institute (ASI) on Nonlinear Phenomena-in Physics and Biology was held at the Banff Centre, Banff, Alberta, Canada, from 17 - 29 August, 1980. The Institute was made possible through funding by the North Atlantic Treaty Organization (who sup­ plied the major portion of the financial aid), the National Research and Engineering Council of Canada, and Simon Fraser University. The availability of the Banff Centre was made possible through the co­ sponsorship (with NATO) of the ASI by the Canadian Association of Physicists. 12 invited lecturers and 82 other participants attended the Institute. Except for two lectures on nonlinear waves by Norman Zabusky, which were omitted because it was felt that they already had been exhaustively treated in the available literature, this volume contains the entire text of the invited lectures. In addition, short reports on some of the contributed talks have also been included. The rationale for the ASI and this resulting volume was that many of the hardest problems and most interesting phenomena being studied by scientists today ar.e nonlinear in nature. The nonlinear models involved often span several different disciplines, °a simple example being the Volterra-type model in population dynamics which has its analogue in nonlinear optics and plasma physics (the 3-wave problem), in the discussion of the social behavior of animals, and in biological competition and selection at the molecular level.

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Content:
Front Matter....Pages i-x
Computation and Innovation in the Nonlinear Sciences....Pages 1-6
Introduction to Nonlinear Waves....Pages 7-82
Remarks on Nonlinear Evolution Equations and the Inverse Scattering Transform....Pages 83-94
The Linearity of Nonlinear Soliton Equations and the Three Wave Resonance Interaction....Pages 95-123
Contour Dynamics: A Boundary Integral Evolutionary Method for Inviscid Incompressible Flows....Pages 125-156
Numerical Computation of Nonlinear Waves....Pages 157-184
Bifurcations, Fluctuations and Dissipative Structures....Pages 185-311
Chemical Oscillations....Pages 313-343
Models in Neurobiology....Pages 345-367
Nonlinear Waves in Neuronal Cortical Structures....Pages 369-400
Bifurcations in Insect Morphogenesis I....Pages 401-450
Bifurcations in Insect Morphogenesis II....Pages 451-484
Selection and Evolution in Molecular Systems....Pages 485-548
Escape from Domains of Attraction for Systems Perturbed by Noise....Pages 549-566
Front Matter....Pages 567-567
Error Propagation in Translation and its Relevance to the Nucleation of Life....Pages 569-570
Pseudopotentials and Symmetries for Generalized Nonlinear Schr?dinger Equations....Pages 571-572
Superposition Principles for Nonlinear Differential Equations....Pages 573-576
On Some Nonlinear Schr?dinger Equations....Pages 577-579
Asymptotic Evaluation Methods of Nonlinear Differential Equations Near the Instability Point....Pages 581-585
Nonlinear Superposition of Simple Waves in Nonhomogeneous Systems....Pages 587-587
Back Matter....Pages 591-609
A Method of Solving Nonlinear Differential Equations....Pages 589-589

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Content:
Front Matter....Pages i-x
Computation and Innovation in the Nonlinear Sciences....Pages 1-6
Introduction to Nonlinear Waves....Pages 7-82
Remarks on Nonlinear Evolution Equations and the Inverse Scattering Transform....Pages 83-94
The Linearity of Nonlinear Soliton Equations and the Three Wave Resonance Interaction....Pages 95-123
Contour Dynamics: A Boundary Integral Evolutionary Method for Inviscid Incompressible Flows....Pages 125-156
Numerical Computation of Nonlinear Waves....Pages 157-184
Bifurcations, Fluctuations and Dissipative Structures....Pages 185-311
Chemical Oscillations....Pages 313-343
Models in Neurobiology....Pages 345-367
Nonlinear Waves in Neuronal Cortical Structures....Pages 369-400
Bifurcations in Insect Morphogenesis I....Pages 401-450
Bifurcations in Insect Morphogenesis II....Pages 451-484
Selection and Evolution in Molecular Systems....Pages 485-548
Escape from Domains of Attraction for Systems Perturbed by Noise....Pages 549-566
Front Matter....Pages 567-567
Error Propagation in Translation and its Relevance to the Nucleation of Life....Pages 569-570
Pseudopotentials and Symmetries for Generalized Nonlinear Schr?dinger Equations....Pages 571-572
Superposition Principles for Nonlinear Differential Equations....Pages 573-576
On Some Nonlinear Schr?dinger Equations....Pages 577-579
Asymptotic Evaluation Methods of Nonlinear Differential Equations Near the Instability Point....Pages 581-585
Nonlinear Superposition of Simple Waves in Nonhomogeneous Systems....Pages 587-587
Back Matter....Pages 591-609
A Method of Solving Nonlinear Differential Equations....Pages 589-589
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