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This is the third Volume in a series of books devoted to the interdisciplinary area between mathematics and physics, all ema nating from the Advanced Study Institutes held in Istanbul in 1970, 1972 and 1977. We believe that physics and mathematics can develop best in harmony and in close communication and cooper ation with each other and are sometimes inseparable. With this goal in mind we tried to bring mathematicians and physicists together to talk and lecture to each other-this time in the area of nonlinear equations. The recent progress and surge of interest in nonlinear ordi nary and partial differential equations has been impressive. At the same time, novel and interesting physical applications mul tiply. There is a unifying element brought about by the same characteristic nonlinear behavior occurring in very widely differ ent physical situations, as in the case of "solitons," for exam ple. This Volume gives, we believe, a very good indication over all of this recent progress both in theory and applications, and over current research activity and problems. The 1977 Advanced Study Institute was sponsored by the NATO Scientific Affairs Division, The University of the Bosphorus and the Turkish Scientific and Technical Research Council. We are deeply grateful to these Institutions for their support, and to lecturers and participants for their hard work and enthusiasm which created an atmosphere of lively scientific discussions.
Table des matières
I - Dynamical Systems and Inverse Scattering Problems.- Integrable Many-Body Problems.- Inverse Scattering Problems for Nonlinear Applications.- Solutions of Nonlinear Equations Simulating Pair Production and Pair Annihilation.- The Two-Time Method Applied to Slowly Evolving Oscillating Systems.- II - Solitons.- Solitons in Physics.- Solitons and Geometry.- Hirota's Method of Solving Soliton-Type Equations.- Prolongation Structure Techniques for the New Hierarchy of Korteweg-de Vries Equations.- Perturbation Theory for the Double Sine-Gordon Equation.- III - Discrete Systems and Continuum Mechanics.- Painlevé Transcendents and Scaling Functions of the Two-Dimensional Ising Model.- Statistical Mechanics of Nonlinear Lattice Dynamic Models Exhibiting Phase Transitions.- Nonlocal Continuum Mechanics and Some Applications.- IV - Nonlinear Field Theories and Quantization.- Quantization of a Nonlinear Field Equation.- Characteristic "Quanta" of Nonlinear Field Equations.- Nonlinear Schrödinger Equation with Sources: An Application of the Canonical Formalism.- Nonlinear Field Equations and Collective Phenomena.- Nonperturbative Self-Interactions, Solitary Waves and Others.- Bound States of Fermions in External and Self-Consistent Fields.
