TY - JOUR
T1 - Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction
AU - Kreiner, Carl Friedrich
AU - Zimmer, Johannes
N1 - Funding Information:
CFK was funded by the MPI for Mathematics in the Sciences, its IMPRS, a DAAD short research grant (D/05/44843), the DFG Priority Program 1095, the University of Bath and an Oberwolfach Leibniz Fellowship. JZ gratefully acknowledges the financial support of the Deutsche Forschungsgemeinschaft through an Emmy Noether grant (Zi 751/1-1), and the EPSRC through an Advanced Research Fellowship (GR/S99037/1).
PY - 2009/5/1
Y1 - 2009/5/1
N2 - The focus of study is the nonlinear discrete sine-Gordon equation, where the nonlinearity refers to a nonlinear interaction of neighbouring atoms. The existence of travelling heteroclinic, homoclinic and periodic waves is shown. The asymptotic states are chosen such that the action functional is finite. The proofs employ variational methods, in particular a suitable concentration-compactness lemma combined with direct minimisation and mountain pass arguments.
AB - The focus of study is the nonlinear discrete sine-Gordon equation, where the nonlinearity refers to a nonlinear interaction of neighbouring atoms. The existence of travelling heteroclinic, homoclinic and periodic waves is shown. The asymptotic states are chosen such that the action functional is finite. The proofs employ variational methods, in particular a suitable concentration-compactness lemma combined with direct minimisation and mountain pass arguments.
KW - Calculus of variations
KW - Concentration compactness
KW - Nonlinear Klein-Gordon lattice
KW - Travelling waves
UR - http://www.scopus.com/inward/record.url?scp=61549089050&partnerID=8YFLogxK
U2 - 10.1016/j.na.2008.04.018
DO - 10.1016/j.na.2008.04.018
M3 - Article
AN - SCOPUS:61549089050
SN - 0362-546X
VL - 70
SP - 3146
EP - 3158
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 9
ER -