Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid

• Published in: IMA journal of applied mathematics Vol. 59; no. 2; pp. 165 - 181
• Main Author: Demiray, H
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.10.1997
• Subjects: Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fluid mechanics: general mathematical aspects; Function theory, analysis; Fundamental areas of phenomenology (including applications); Hydrodynamic waves; Mathematical methods in physics; Partial differential equations; Physics; Modulation instability; Nonlinear equations; Prestressed material; Wave propagation; Partial differential equations; Non viscous fluid; Wave modulation; Elastic material; Schroedinger equation; Incompressible fluid; Elastic deformation
• ISSN: 0272-4960; 1464-3634
• DOI: 10.1093/imamat/59.2.165

In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approxiamte equations of an incompressible inviscid fluid, and then utilizing the reductive perturbation technique the amplitude modulation of weakly nonlinear waves is examined. It is shown that equation. The result is compared with some previous works on the same subject. The modulation instablity of the monochromatic wave solution is discussed for some elastic materials and initial deformation.