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.

在给定的预应力条件下，充满流体的弹性管中的孤立波被限制在背景流体速度和波速的相当狭窄的组合中。该集合（我们称为存在域）由代表各种物理和数学限制的几条曲线界定。值得注意的是，这些限制条件可以看作是纯代数条件，强加于微分方程的控制系统。物理限制中最重要的是避免皱纹和波浪形的自渗透性。尤其是，严格确定了即将起皱的临界波速的存在，与背景流体速度无关。