Nonlinearity, Integrability and All That: Twenty Years After Needs '79 - Proceedings of the Workshop

PREFACE
 CONTENTS
 Part I Advances in Analytical Methods
 NEVANLINNA THEORY AND DIFFERENCE EQUATIONS OF PAINLEVE TYPE
 1 Introduction
 2 Complex Difference Equations
 3 Nevanlinna Theory
 3.1 The Nevanlinna Characteristic
 3.2 The Order of a Meromorphic Function
 3.3 Finite-Order Solutions of Differential and Difference Equations
 4 Series Methods
 5 Discussion
 References
 MONODROMY TRANSFORM APPROACH TO SOLUTION OF SOME FIELD EQUATIONS IN GENERAL RELATIVITY AND STRING THEORY
 1 Introduction
 2 Generalized Ernst equations
 3 Equivalent \"\"spectral\"\" N x N --
matrix problem. 4 Direct problem of the monodromy transform and definition of the monodromy data5 Inverse problem of the monodromy transform and equivalent singular integral equations
 6 Equivalent Fredholm equation: the existence and uniqueness of local solutions for arbitrary chosen monodromy data
 Acknowledgments
 References
 NONLINEAR SIGMA MODEL ON CURVED SURFACES:ENERGY AND ANHOLONOMY
 1 Introduction
 2 Hamiltonian for the model on a curved surface
 3 The Bogomol\'nyi inequality and its generalization
 4 Equations for local energy minima and exact solutions. 5 Two branch structure of geometric phase and energy6 Applications
 References
 A NONLINEAR DISCRETE SYSTEM SOLVABLE ON THE FINITE DOMAIN *
 1 Introduction
 2 Discrete SRS system
 3 The Lax pair
 4 Explicit solution for infinite medium
 5 Solution of the finite domain
 References
 SOME NONDECAYING POTENTIALS FOR THE NONSTATIONARY SCHRODINGER EQUATION *
 1 Introduction
 Binary Backlund Transformations
 2 Recursion Procedure
 3 Resolution of the recursion relations
 4 Properties of potentials
 References
 SOME NONDECAYING POTENTIALS FOR THE HEAT CONDUCTION EQUATION *
 1 Introduction. 2 On Jost solutions3 Binary Backlund transformations
 4 Two solitons on a generic background
 References
 A GEOMETRICAL APPROACH TO THE EMDEN-FOWLER EQUATION
 1 Introduction
 2 Preliminaries
 Acknowledgments
 References
 MULTI-SOLITON SOLUTIONS OF THE GENERALIZED WEIERSTRASS SYSTEM
 1 The Generalized Weierstrass System and Associated Sigma Model
 2 The Auto-BT for the Generalized Weierstrass System
 3 Multi-Soliton Solutions
 3.1 Algebraic multi-soliton solutions of the GW system
 3.2 Periodic multi-soliton solutions of GW system.
 Acknowledgments
 References. CHARACTERISTIC VARIABLES FOR A COMPLETELY INTEGRABLE SHALLOW WATER EQUATION1 Introduction
 2 Crossing of characteristics
 3 The isospectral problem
 4 Finite dimensional systems
 Conclusions
 Acknowledgments
 References
 BILINEAR FORMALISM FOR SUPERSYMMETRI KdV-TYPE EQUATIONS
 1 Introduction
 2 Standard bilinear formalism
 3 Supersymmetry
 4 Super-Hirota operators
 5 Bilinear SUSY KdV-type equations
 Acknowledgments
 References
 RATIONAL SOLUTIONS OF A MIXED KdV+mKdV AND BENJAMIN-ONO EQUATION
 1 Introduction
 2 Continuum limit
 3 Exact bilinearization
 4 Conclusions
 Acknowledgments.