Analytical Methods in
Nonlinear Wave Theory
By I.A. Molotkov
275 pages, 6” x 8 ½”
The book is devoted to the development and description of analytical methods for this important branch of nonlinear physics – the theory of localized wave processes. The application of each method described in the book is illustrated by the solutions of concrete problems. The spectrum of these problems is very wide.
Among them are the following: propagation and self-action of powerful wave beams in inhomogenous media, propagation of intense acoustic beams, ultrashort pulses in nonlinear graded-index light guides, waves in media with internal structure, and long surface gravitational waves in fluids with variable depth.
These topics are treated in detail. The book is addressed to specialists in theoretical physics who study nonlinear phenomena in radiophysics, acoustics, optics, plasma theory, and geophysics; to specialists in mathematical physics, as well as to postgraduate students and students in corresponding specialties.
Derivation & transformation of certain nonlinear equations.
Perturbation of the exact solution.
Variations of the parameters of unperturbed soliton.
Perturbation methods in absence of the exact solution. (Whitham’s Principle).
Trajectory Variational Principles.
Small distances (times). Analysis of the Cauchy problems.
Nonlinear interaction of the principle & impurity solitary waves. The approximation of small amplitudes. Excitation of multiple phases.
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