Solitons in Mathematics and Physics

The soliton is a dramatic concept in nonlinear science. What makes this book unique in the treatment of this subject is its focus on the properties that make the soliton physically ubiquitous and the soliton equation mathematically miraculous. Here, on the classical level, is the entity field theorists have been postulating for years: a local traveling wave pulse; a lump-like coherent structure; the solution of a field equation with remarkable stability and particle-like properties. It is a fundamental mode of propagation in gravity- driven surface and internal waves; in atmospheric waves; in ion acoustic and Langmuir waves in plasmas; in some laser waves in nonlinear media; and in many biologic contexts, such as alpha- helix proteins.

The History of the Soliton; Derivation of the Korteweg-de Vries, Nonlinear Schrodinger and Other Important and Canonical Equations of Mathematical Physics; Soliton Equation Families and Solution Methods; The -Function, the Hirota Method, the Painleve Property and Backlund Transformations for the Korteweg-de Vries Family of Soliton Equations; Connecting Links among the Miracles of Soliton Mathematics.