Analytical representations suitable to analyze the nonrepetitive pulse-like temporal behavior of physical quantities are derived. The representation utilizes solutions of a linear model equation in which the temporal variation is subject to time-dependent driving and dissipative forces. The property of solutions is described, and it is shown that such representations can provide a basis for quantitative comparisons of behaviors and a basis for physically meaningful interpretations of the results. Observations of solar flares in the soft x-ray flux have been analyzed with this method.