Solitons

by Bullough, Robin K. Caudrey, Philip J.

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Title Statements

Full title :Solitons / edited by Robin K. Bullough, Philip J. Caudrey.

Summary

Until the beginning of this decade the number of significant exactly soluble problems in physics was limited to a very few: the classical or quanti sed harmonic oscillator, the linearised many-body problem, the quanti sed hydrogen atom, Newton's solution of the planetary orbit problem, Onsager's solution of the two-dimensional Ising problem, almost exhaust the list. Now the situation is quite different. We have a large number of exactly soluble nonlinear systems of physical significance and the number of these is growing steadily. Recent examples include a limited solution of Ein stein's field equations!, an apparently exact solution of the quantised sine-Gordon 2 equation u - U = sin(u) which establishes connections with the Ising models, xx tt 3 and a solution of the equations of motion of a rigid body in g dimensions . This book is concerned with problems such as these. But more specifically it is concerned with solitons. These mathematical objects are exact, analytical, solutions of nonlinear wave or evolution equations like the sine-Gordon equation (s-G) or the Korteweg-de Vries equation (KdV) u + 6uu + u = O. The discovery by Gardner, t x xxx.

Edition Statements

Publication Date:1980.

Publication Statements

Publisher(s):Springer Berlin Heidelberg
Place of Publication:Berlin, Heidelberg
Language:eng
Publication Date:1980.

The Physical Object

Description:1 online resource

Edition Identifiers

ISBN:9783642814488, 3642814484, 9783642814501, 3642814506
DOI:10.1007/978-3-642-81448-8
oclc:ocn913666513
LC Classification:QC19.2-20.85
Dewey Decimal:530.1

1 The Soliton and Its History -- 1.1 Russell's Discovery of the 'Great Solitary Wave' -- 1.2 Definition of a Soliton: N-Soliton Solutions of Nonlinear Evolution Equations -- 1.3 Bäcklund Transformations and Conserved Densities -- 1.4 Other Physical Problems and the Discovery of the Inverse Method -- 1.5 Operator Pair Formulation of Nonlinear Evolution Equations -- 1.6 Discovery of Some Other N-Soliton Solutions: The AKNS-Zakharov-Shabat 2 x 2 Scattering Scheme and Its Geometry -- 1.7 Further Progress on Inverse Scattering Methods -- References -- 2. Aspects of Soliton Physics -- 2.1 Historical Remarks and Summary -- 2.2 Model Interacting Systems -- 2.3 Inverse Spectral Transformation and Motion Invariants -- Appendix A: Formal Derivation of the Marchenko Equations -- References -- 3. The Double Sine-Gordon Equations: A Physically Applicable System of Equations -- 3.1 Physical Background -- 3.2 Theory of Degenerate SIT -- 3.3 Spin Waves in Liquid 3He -- 3.4 Perturbation Theory for the Double Sine-Gordon Equation -- References -- 4. On a Nonlinear Lattice (The Toda Lattice) -- 4.1 Nonlinear Lattices -- 4.2 The Exponential Interaction -- 4.3 Matrix Formalism -- 4.4 The Continuum Limi…