An Integrable Three Particle System Related to Intrinsic Localized Modes in Fermi-Pasta-Ulam-β Chain(Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics and Fluid Mechanics)
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In this paper, a ring of three particles interacting via nearest-neighbor harmonic and quartic potentials is investigated for the study of intrinsic localized modes (ILMs) in Fermi-Pasta-Ulam (FPU) atomic chain. In spite of the fact that above Hamiltonian system has been shown to be integrable by Hietaniata [Phys. Rep. 147 (1987) 87], Yoshida and Ramani [Physica D 30 (1988) 151], respectively, we approve its integrability in a more straightforward way. Moreover, we obtain exact periodic solutions in terms of the Jacobi elliptic functions for both the zero and nonzero third first integral. The significance of these findings lies in the fact that analytical stationary and moving ILMs solutions are obtained, and a close relationship between the movability of ILMs and the third first integral is clarified.