Nonlinear Evolution Equations And Dynamical Systems Needs 94

Proceedings of the 6th International Workshop, 16-26 July 1990, Dubna, USSR

Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.

The Workshop NEEDS '91 brought together, from all over the world, scientists engaged in research on nonlinear systems, either their underlying mathematical properties or their physical applications. Accordingly, many talks were devoted to present methods of solution (like spectral transform) and to the investigation of structural (geometrical and/or algebraic) properties of (continuous and discrete) nonlinear evolution equations. Peculiar nonlinear systems, such as cellular automata, were also discussed. Applications to various fields of physics, namely, quantum field theory, fluid dynamics, general relativity and plasma physics were considered.

NEEDs '92 was held in Dubna, Russia in July 1992. This set of proceedings compiles the lectures and short contributions on the soliton theory and its applications presented during the conference. The topics covered included the most recent results on relevant problems of nonlinear evolution systems such as: Multidimensional Integrable Systems, Geometric and Algebraic Methods, Painleve Property, Lie-Backlund Symmetries, Spectral Methods, Solitons and Coherent Structures, Computational Methods, Quantum Field and String Theories, Nonlinear Optics and Hydrodynamics, Condensed Matter etc. The extent of coverage for these important topics makes this book useful, informative and insighful for the mathematics and theoretical physics community, both the senior researches and those just entering the field.