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Home > Science, Technology & Agriculture > Technology: general issues > Maths for engineers > Nonlinear Evolution Equations: (180 Pitman Research Notes in Mathematics Series)
Nonlinear Evolution Equations: (180 Pitman Research Notes in Mathematics Series)

Nonlinear Evolution Equations: (180 Pitman Research Notes in Mathematics Series)


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About the Book

This series aims to disseminate important new material of a specialist nature in economic form. It is designed to cover the whole spectrum of mathematics and also reflect the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. This work describes contemporary understanding of the modelling of nonlinear wave processes in weakly dispersive media. The notion of evolution equations governing the propagation of single waves is used and three methods are described for constructing nonlinear equations: the iterative, the asymptotic and the spectral. A comparative analysis of these methods is presented, including the problems of their convergence and correctness. Several physical situations are discussed involving one-dimensional, weakly inhomogeneous and/or wave-guide systems. The simple evolution equations are analyzed separately. This work is designed to be of interest to graduate students and researchers working in the areas of nonlinear wave theory and mathematical physics.

Table of Contents:
Part 1 Singular methods of simplification for one-dimensional wave processes: the iterative and asymptotic methods; asymptotic series for interacting waves; the spectral method; strongly nonlinear systems; the comparative estimation of accuracy. Part 2 The quasiplane waves in nonliner media and the evolution equations: the asymptotic scheme for propagation along linear and nonlinear rays; the estimation of nonlinear effects in a near-caustic zone; the asymptotic scheme for wave-beams; wave-beams in weakly inhomogeneous media. Part 3 The wave-guides and evolution equations: the Galerkin procedure for eliminating the "non-wave" coordinate; the asymptotic method for the one-wave approximation; wave-guides of complicated structures. Part 4 Applications - simple evolution equations: the equation of a simple wave; the Burgers equation; an integro-differential equation; the equations of nonlinear rays.


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Product Details
  • ISBN-13: 9780582013148
  • Publisher: Longman
  • Publisher Imprint: Longman Higher Education
  • Height: 250 mm
  • Weight: 271 gr
  • ISBN-10: 0582013143
  • Publisher Date: /09/1988
  • Binding: Paperback
  • Series Title: 180 Pitman Research Notes in Mathematics Series
  • Width: 170 mm


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