On the Korteweg–de Vries Limit for the Fermi–Pasta–Ulam System

In this paper, we develop dispersive PDE techniques for the Fermi–Pasta–Ulam (FPU) system with infinitely many oscillators, and show that general solutions to infinite FPU can be approximated by counter-propagating waves governed Korteweg–de Vries (KdV) equation as lattice spacing approaches zero. Our result not only simplifies hypotheses but also reduces regularity requirement in previous study (Schneider Wayne, In: International conference on differential equations, Berlin, 1999, World Sci. Publ, River Edge, NJ, Vol 1, 2, pp 390–404, 2000).