Abstract:  In the talk I discuss a class of rather interesting solutions of integrable systems that I call harmonic breathers. These solutions arise as nonlinear analogues of exp[i(kx - ω(k)t))], in the sense that a huge class of solutions of integrable systems corresponding to the continuous spectrum of the associated Lax pair can be decomposed into these solutions just like solutions of linear evolution PDEs are decomposable into exp[i(kx - ω(k)t)] by means of the Fourier transform. Unlike the Fourier decomposition, the decomposition into harmonic breathers though is nonlinear with a whole bunch of new properties. Harmonic breathers also provide an example of wave-particle duality different from that of Heisenberg. Last but not least harmonic breathers exhibit behavior observed in real life situations.