Solitons and Particles

The following sections are included:

• PREFACE

• CONTENTS

Solitons made their first appearance in the world of science with the beautiful report on waves, presented by J. Scott Russell in 1842 and 1843 at the British Association for the Advancement of Science [1]^a:

“I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped — not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon …“…

The following sections are included:

• Introduction

• Introductory Bibliography Notes on the IST Method

• The Estabrook-Wahlquist Prolongation Method

• The Symmetry Approach

• References for Section 2

• References for Section 2 — Books

The following sections are included:

• One-dimensional Systems

• Vortices and Two-dimensional Systems

• Monopoles and Three-dimensional Solitons

• Four-dimensional Solitons: Instantons

• References for Section 3

• References for Section 3 — Books and Reviews

The section consist of reprinted papers in the following topics:

• INTERACTION OF “SOLITONS” IN A COLLISIONLESS PLASMA AND THE RECURRENCE OF INITIAL STATES

• METHOD FOR SOLVING THE KORTEWEG-deVRIES EQUATION

• Integrals of Nonlinear Equations of Evolution and Solitary Waves

• Method for Solving the Sine-Gordon Equation

• General Derivation of Backlund Transformations from Inverse Scattering Problems

• ON RELATIVISTIC-INVARIANT FORMULATION OF THE INVERSE SCATTERING TRANSFORM METHOD

• Canonical Structure of Soliton Equations via Isospectral Eigenvalue Problems

• Coupled Nonlinear Evolution Equations Solvable Via the Inverse Spectral Transform, and Solitons that Come Back: the Boomeron

• Solution by the Spectral-Transform Method of a Nonlinear Evolution Equation Including as a Special Case the Cylindrical KdV Equation

• EXACT THEORY-OF TWO-DIMENSIONAL SELF-FOCUSING AND ONE-DIMENSIONAL SELF-MODULATION OF IVAVES IN NONLINEAR MEDIA

• Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method

• Bäcklund Transformation for Solutions of the Korteweg–de Vries Equation

• Prolongation structures of nonlinear evolution equations

• Prolongation structures of nonlinear evolution equations II

• Prolongation analysis of the cylindrical Korteweg-de Vries equation

• Nonlinear evolution equations and nonabelian prolongations

• Bäcklund transformations and the symmetries of the Yang equations

• Inverse scattering problems in higher dimensions: Yang–Mills fields and the supersymmetric sine-Gordon equation

• “IST-solvable” nonlinear evolution equations and existence—An extension of Lax’s method^a)

• Evolution equations possessing infinitely many symmetries

• SYMPLECTIC STRUCTURES, THEIR BACKLUND TRANSFORMATIONS AND HEREDITARY SYMMETRIES

• A simple model of the integrable Hamiltonian equation^a)

• Some New Conservation Laws

• Kinks

• Sine-Gordon Equation

• Nonperturbative methods and extended-hadron models in field theory II: Two-dimensional models and extended hadrons

• Quantization of nonlinear waves

• Soliton quantization

• Quantum sine-Gordon equation as the massive Thirring model

• Solitons with fermion number 1/2

• Soliton excitations in polyacetylene

• On the Magnetic Properties of Superconductors of the Second Group

• VORTEX-LINE MODELS FOR DUAL STRINGS

• Classical vortex solution of the Abelian Higgs model

• The stability of classical solutions

• Interaction energy of superconducting vortices

• Arbitrary N-Vortex Solutions to the First Order Ginzburg-Landau Equations

• Fractional charge and zero modes for planar systems in a magnetic field

• A 1/n EXPANDABLE SERIES OF NON-LINEAR σ MODELS WITH INSTANTONS

• SCATTERING OF MASSLESS LUMPS AND NON-LOCAL CHARGES IN THE TWO-DIMENSIONAL CLASSICAL NON-LINEAR σ-MODEL

• Factorized S-Matrices in Two Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Theory Models

• The Theory of Magnetic Poles

• A UNIFIED FIELD THEORY OF MESONS AND BARYONS

• MAGNETIC MONOPOLES IN UNIFIED GAUGE THEORIES

• Particle spectrum in quantum field theory

• Poles with both magnetic and electric charges in non-Abelian gauge theory

• Exact Classical Solution for the ’t Hooft Monopole and the Julia-Zee Dyon

• Class of scalar-field soliton solutions in three space dimensions

• Quantum expansion of soliton solutions

• Canonical quantization of nonlinear waves

• SOLITON QUANTIZATION IN GAUGE THEORIES

• Fractional Quantum Numbers on Solitons

• Spin from Isospin in a Gauge Theory

• Fermion-Boson Puzzle in a Gauge Theory

• Connection of Spin and Statistics for Charge-Monopole Composites

• CURRENT ALGEBRA, BARYONS, AND QUARK CONFINEMENT

• STABILITY ANALYSIS FOR SINGULAR NON-ABELIAN MAGNETIC MONOPOLES

• EXACT MULTIMONOPOLE SOLUTIONS IN THE BOGOMOLNY–PRASAD–SOMMERFIED LIMIT

• GENERATING MONOPOLES OF ARBITRARY CHARGE BY BÄCKLUND TRANSFORMATIONS

• Monopoles and dyons in the SU(5) model

• Cosmological Production of Superheavy Magnetic Monopoles

• Cosmological Density Fluctuations Produced by Vacuum Strings

• ADLER-BELL-JACKIW ANOMALY AND FERMION-NUMBER BREAKING IN THE PRESENCE OF A MAGNETIC MONOPOLE

• Dyon-fermion dynamics

• PSEUDOPARTICLE SOLUTIONS OF THE YANG-MILLS EQUATIONS

• Symmetry Breaking through Bell-Jackiw Anomalies

• Computation of the quantum effects due to a four-dimensional pseudoparticle

• Vacuum Periodicity in a Yang-Mills Quantum Theory

• THE STRUCTURE OF THE GAUGE THEORY VACUUM

• DYONS OF CHARGE eθ/2π

• Condition of Self-Duality for SU(2) Gauge Fields on Euclidean Four-Dimensional Space

• Some aspects of the linear system for self-dual Yang-Mills fields

• SELF-DUAL YANG-MILLS AS A TOTALLY INTEGRABLE SYSTEM

• Instantons and Algebraic Geometry

• CONSTRUCTION OF INSTANTONS

• A Yang–Mills–Higgs Monopole of Charge 2