We show that particular solutions of certain nonlinear field equations can be constructed using Bäcklund transformations, recursion and Bessel functions. It is well-know n that the m odified Bessel differential equation [ 1] d w + 1 dw d r r d r 1 + w = 0 admits as solution the modified Bessel function 1 2 — r 4 v = 0 n\ r (n + 5 + 1) (1) (2)