edited by Boris A Kupershmidt (Univ. Tennessee Space Inst.)

Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.

• The Main Soliton Theorem (I Cherednik)
• Functional Bethe Ansatz (E K Sklyanin)
• Integrability in Models of Two-Dimensional Turbulence (Y Murometz & S Razboynick)
• Solitons, Numerical Chaos and Cellular Automata (M J Ablowitz et al.)
• The Unstable Nonlinear Schrödinger Equation (T Yajima & M Wadati)
• Classification of Integrable Equations (R K Dodd)
• List of All Integrable Hamiltonian Systems of General Type with Two Degrees of Freedom (A T Fomenko)
• Finite-Dimensional Soliton Systems (S N M Ruijsenaars)
• Relativistic Analogs of Basic Integrable Systems (J Gibbons & B A Kupershmidt)
• Liouville Generating Functions for Isospectral Flows in Loop Algebras (M R Adams et al.)
• A Loop Algebra Decomposition for Korteweg-de Vries Equations (R J Schilling)
• Energy Dependent Spectral Problems: Their Hamiltonian Structures and Miura Maps (A P Fordy)
• Commuting Differential Operators Over Integrable Hierarchies (F Guil)
• Lie Superalgebra Structure on Eigenfunctions, and Jets of the Resolvent's Kernal Near the Derivative and the Bott Cocycle (A O Radul)
• Super Miura Transformations, Super Schwarzian Derivatives and Super Hill Operators (P Mathieu)