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Unimodal wavetrains and solitons in convex Fermi–Pasta–Ulam chains

2010; Cambridge University Press; Volume: 140; Issue: 4 Linguagem: Inglês

10.1017/s0308210509000146

1473-7124

Michael Herrmann,

Advanced Mathematical Physics Problems

We consider atomic chains with nearest neighbour interactions and study periodic and homoclinic travelling waves which are called wave trains and solitons, respectively. Our main result is a new existence proof which relies on the constrained maximisation of the potential energy and exploits the invariance properties of an improvement operator. The approach is restricted to convex interaction potentials but refines the standard results as it provides the existence of travelling waves with unimodal and even profile functions. Moreover, we discuss the numerical approximation and complete localization of wave trains, and show that wave trains converge to solitons when the periodicity length tends to infinity.