The phenomenon of recurrence in nonlinear systems with many degrees of freedom was first observed in the classical numerical experiments by Fermi, Pasta, and Ulam [1] in 1954. <...> The idea of Fermi was to address how randomization due to the nonlinear interaction leads to the energy equipartition between large number of degrees of freedom in the mechanical chain. <...> The chain in [1] had a quadratic nonlinearity and included 64 oscillators supplemented with long-wave initial conditions. <...> Instead of the anticipated energy equipartition, numerical experiments showed that after a finite time a recurrence to the initial data was achieved accompanied by a quasi-periodic energy exchange between several initially exited modes. <...> That recurrence phenomenon became known as the famous Fermi–Pasta–Ulam (FPU) problem and has been one of the central problems of the nonlinear science, studied in numerous papers. <...> Many other peculiarities of this problem have been discovered and studied (for more details, see the original papers [2] published before the era of integrability for nonlinear systems). <...> Since the discovery of the Inverse Scattering Transform, which was first applied to the KDV equation [3], and later to the nonlinear Schrodinger equation (NLSE) [4], many aspects of the FPU recurrence became more clear. <...> The FPU recurrence was also intensively studied experimentally (the first experimental demonstration in optical fibers of the FPU recurrence was presented in [6]). <...> The main goal of this paper is to explain how the recurrence phenomenon appears within the onedimensional NLSE iψt +ψxx +2|ψ|2ψ = 0. 1)e-mail: kuznetso@itp.ac.ru 108 (1) This equation with a reasonable accuracy describes propagation of optical solitons in fibers. <...> At the present time, there are known many exact solutions of the NLSE which describe propagation of solitons/breathers on the condensate background. <...> Such solution was constructed for a first time in [7] and later inmany other papers (see [8] and references therein). <...> All these solutions show that after a while the condensate recovers its amplitude but has a different (but constant) phase. <...> This is the analogue of the FPU recurrence for the NLSE (see recent numerical confirmations [9] for arbitrary initial conditions). <...> In this paper we give a qualitative explanation of the FPU analog for cnoidal waves. <...> To find the cnoidal wave to Eq. (1) one <...>