Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices

Kirillov, Oleg (2010) Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices. Zeitschrift für angewandte Mathematik und Physik, 61 (2). pp. 221-234. ISSN 0044-2275

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Official URL: http://dx.doi.org/10.1007/s00033-009-0032-0

Abstract

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter and on the vector of real physical parameters p. We study perturbations of semi-simple multiple eigenvalues as well as perturbations of non-derogatory eigenvalues under small variations of p. Explicit formulae describing the bifurcation of the eigenvalues are derived. Application to the problem of excitation of unstable modes in rotating continua such as spherically symmetric MHD alpha-alpha-dynamo and circular string demonstrates the efficiency and applicability of the approach.

Item Type: Article
Uncontrolled Keywords: Operator matrix, Non-self-adjoint boundary eigen value problem, Keldysh chain, Multiple eigenvalue, Diabolical point, Exceptional
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Oleg Kirillov
Date Deposited: 23 Jan 2017 12:23
Last Modified: 23 Jan 2017 12:23
URI: http://nrl.northumbria.ac.uk/id/eprint/29285

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