The physics-mathematic equation of dynamic-shape curves is deduced for fused tapering optical fibers in this paper. The close-form solution of the equation is acquired by its concrete initial boundary and volume-conservation conditions. For arbitrary-parameter torches,the dynamic-tapering-shape curves in different tapering processes are described by the solution in a convenient, accurate and integrative manner. Furthermore, the dynamictapering coupling processes for several fused devices can be described accurately. Thus, the dynamic coupling curves and their relative spectra of the fused optical fiber devices, such as optical fiber couplers,wavelength division multiplexers,filters and so on,can be calculated by the formula deduced in this paper. A large quantity of experimental data with their relevant charts have been provided, and they coincide perfectly with the theoretical results. Especially, if the initial length of the fused area is known, the solution can predict the tapering shape curve for arbitrary elongating length.