We study the well-known one-dimensional problem of 𝑁 particles with nonlinear interaction. The 𝛽-Fermi–Pasta–Ulam model is the special case of quadratic and quartic interaction potential among nearest neighbours. We enumerate and classify the simple periodic orbits for this system and find the stability zones, employing Floquet theory. We quantize the nonlinear normal modes and construct a wavefunction for what we believe is a primitive nonlinear analogue of a `phonon’.
Volume 93 | Issue 5
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