TY - JOUR
T1 - Travelling lattice waves in a toy model of Lennard-Jones interaction
AU - Venney, Christine R.
AU - Zimmer, Johannes
PY - 2014/3/1
Y1 - 2014/3/1
N2 - We consider an infinite lattice model, where particles interact with nearest neighbour (NN) and next-to-nearest neighbours (NNN); the NN and NNN springs act against each other to mimic the Lennard-Jones potential. The existence of subsonic waves homoclinic to exponentially small periodic oscillations is shown as well as the existence of supersonic periodic solutions. The proofs rely on methods from normal form and centre space analysis for the homoclinic solutions and centre manifold analysis for the periodic solutions.
AB - We consider an infinite lattice model, where particles interact with nearest neighbour (NN) and next-to-nearest neighbours (NNN); the NN and NNN springs act against each other to mimic the Lennard-Jones potential. The existence of subsonic waves homoclinic to exponentially small periodic oscillations is shown as well as the existence of supersonic periodic solutions. The proofs rely on methods from normal form and centre space analysis for the homoclinic solutions and centre manifold analysis for the periodic solutions.
UR - http://www.scopus.com/inward/record.url?scp=84894664641&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1090/S0033-569X-2013-01320-4
U2 - 10.1090/S0033-569X-2013-01320-4
DO - 10.1090/S0033-569X-2013-01320-4
M3 - Article
AN - SCOPUS:84894664641
SN - 0033-569X
VL - 72
SP - 65
EP - 84
JO - Quarterly of Applied Mathematics
JF - Quarterly of Applied Mathematics
IS - 1
ER -