Evolution of perturbations on a weakly inhomogeneous background

• Published in: Journal of applied mathematics and mechanics Vol. 71; no. 5; pp. 690 - 700
• Main Authors: Kulikovskii, A.G., Lozovskii, A.V., Pashchenko, N.T.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2007; New York, NY Elsevier Science
• Subjects: Exact sciences and technology; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Saddle point method; Wave amplification; Initial value problem; Hamiltonian mechanics; Asymptotic approximation; Modeling; Stationary condition; Wave dispersion
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/j.jappmathmech.2007.11.002

The evolution of growing and decaying one-dimensional linear perturbations on a stationary, weakly inhomogeneous background is investigated studied. Attention is focused on the amplification of waves that arise from initial perturbations, localized in regions whose width is small compared with the inhomogeneity scale. A relation between the Hamiltonian formalism (with a complex dispersion equation) and the saddle-point method is established for an asymptotic representation of the integral that expresses perturbations in terms of the initial data. Model examples of the evolution of perturbations are examined.