The nonlinear physical systems which are described by infinite dimensional integrable equations have two types of solutions: solitons which can be viewed as nonlinear localized ‘‘normal modes’’ and radiation solution which can be viewed as linear modes (termed as phonons, photons, spin waves, etc., in condensed matter physical systems). These linear modes are modulationally unstable to nonlinear normal modes and this instability is expressed by a time domain decay of their amplitude ast−1/2, which corresponds to 1/fspectrum. This mechanism is explored for three types of nonlinear equations and an analogy with 1/fnoise generated as a result of low‐frequency bremsstrahlung is revealed.