Physics – Mathematical Physics
Scientific paper
2009-01-23
Proc. R. Soc. Edinb. Sect. A-Math., vol. 140, no. 4, pp. 753-785, 2010
Physics
Mathematical Physics
27 pages, several figures
Scientific paper
10.1017/S0308210509000146
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.
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