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Under given prestress conditions, solitary waves in fluid-filled elastic tubes are confined to a rather narrow set of combinations of the background fluid velocity and the wave speed. This set, which we call the domain of existence, is bounded by several curves that represent various physical and mathematical restrictions. Remarkably, these restrictions can be cast as purely algebraic conditions to be imposed upon the governing system of differential equations. Paramount among the physical restrictions are the avoidance of wrinkles and the self-impenetrability of the wave profile. In particular, the existence of a critical wave speed of impending wrinkling, independent of the background fluid velocity, is established rigorously. [ABSTRACT FROM AUTHOR]

Provides information on a study which explained the evolution of the material structure for materials of first and second order in terms of first-order differential equations for a set of `transplant' maps. Bodies and configurations; Second-order material points; Explanation on evolution laws.

Discusses differential equation for the amplitude of wrinkles. Derivation of the equation; Relationship between wrinkling strain, curvature, amplitude and wavelength; Obtaining a nonlinear ordinary differential equation governing the amplitude of the wrinkles.