Solutions Manual (Mathematical Methods for Physicists) - Softcover

Eilenberger, G.

Softcover

ISBN 10: 038710223X ISBN 13: 9780387102238

Publisher: Springer-Verlag New York Inc., 1983

Synopsis

1.1 Why Study Solitons? The last century of physics, which was initiated by Maxwell's completion of the theory of electromagnetism, can, with some justification, be called the era of linear physi cs. ~Jith few excepti ons, the methods of theoreti ca 1 phys­ ics have been dominated by linear equations (Maxwell, Schrodinger), linear mathematical objects (vector spaces, in particular Hilbert spaces), and linear methods (Fourier transforms, perturbation theory, linear response theory) . Naturally the importance of nonlinearity, beginning with the Navier-Stokes equations and continuing to gravitation theory and the interactions of par­ ticles in solids, nuclei, and quantized fields, was recognized. However, it was hardly possible to treat the effects of nonlinearity, except as a per­ turbation to the basis solutions of the linearized theory. During the last decade, it has become more widely recognized in many areas of "field physics" that nonlinearity can result in qualitatively new phenom­ ena which cannot be constructed via perturbation theory starting from linear­ ized equations. By "field physics" we mean all those areas of theoretical physics for which the description of physical phenomena leads one to consider field equations, or partial differential equations of the form (1.1.1) ~t or ~tt = F(~, ~x ... ) for one- or many-component "fields" Ht,x,y, ... ) (or their quantum analogs).

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 1983
• Language: English
• ISBN 10: 038710223X
• ISBN 13: 9780387102238
• Binding: Paperback
• Number of pages: 192