The nonlinear integral equation \[ \int^{+\infty}_{-\infty} p(s) p(s+ t) p(s+\tau)\, ds= h(t,\tau) \] is transformed into the functional equation \(P(x)P(\xi)\overline{P(x+\xi)}= H(x,\xi)\) using the Fourier transform. The latter equation is solved explicitly under suitable conditions being necessary and sufficient. Two examples are given.