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Title: Some aspects of the theory of the propagation of nonlinear waves in unstable media
Author: Pawlik, Marek
ISNI:       0000 0001 3479 3203
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1977
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The behaviour of waves in stable and unstable media in the nonlinear regime is of considerable interest and relevance to many physical systems. New, tractable techniques are required to account for the possible interactions of dispersive, dissipative and modulational effects and their effects on the propagation of nonlinear waves. The reductive perturbation technique an asymptotic expansion in multiple time and space scales — is extended to apply to wave propagation in unstable media in both one and two dimensions. It is shown that, to lowest order, the wave amplitude satisfies a form of nonlinear Schrödinger equation and the validity of this equation is established for a much wider class of systems than was previously supposed. Explicit expressions are given for determining the complex coefficients of this equation from the coefficients of the system of equations describing the original physical system. These general methods are applied to two physical systems. A nonlinear theory of the propagation of acoustic waves in piezoelectric semiconductors is presented and an explicit solution of the relevant generalised nonlinear Schrödinger is found using a perturbation technique. This solution is found to be an envelope soliton and theoretically confirms domain propagation in piezoelectric semiconductors. A nonlinear theory of a two-stream instability in a marginally stable state is given and the wave equation is found to be a different form of the nonlinear Schrödinger equation. The nonlinear effects are found to enhance rather than suppress the instability in agreement with previously published results. A discussion is given of the stability of inhomogeneous plasma streams in mutually perpendicular electric and magnetic fields and suggestions are made for the development of a nonlinear theory of such systems using the general techniques developed.
Supervisor: Not available Sponsor: Science Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics ; QC Physics