Spin waves or magnons represent elementary excitations of magnetically ordered materials. In the field of magnonics, spin waves are expected to be used as information carriers, taking advantage of their short wavelengths compared to electromagnetic waves possessing similar frequencies. The formation of noncollinear spin configurations such as domain walls, vortices or magnetic skyrmions is a natural way of influencing the properties of magnons in a system. Spin waves are often described within the terms of the classical Landau-Lifshitz-Gilbert equation. Here we discuss how the noncollinear spin arrangement forces the spin waves to be cylindrically instead of circularly polarized, leading to an enhancement of the effective damping parameter compared to the Gilbert damping . The results are illustrated through the example of isolated k\pi skyrmions , which represent cylindrically symmetric two-dimensional localized spin configurations where the out-of-plane component of the magnetization rotates by k\pi between the center of the structure and the collinear background. At higher temperatures, magnon-magnon interactions lead to a modification of spin wave frequencies, which can be taken into account in a micromagnetic model by introducing effective temperature-dependent interaction parameters. Through the example of a ferromagnetic system, we calculate the temperature dependence of the effective Dzyaloshinsky-Moriya interaction , which also plays a crucial role in the stabilization of noncollinear magnetic structures.