Abstract
The existence of travelling heteroclinic waves for the sine-Gordon lattice is proved for a linear interaction of neighbouring atoms. The asymptotic states are chosen such that the action functional is finite. The proof relies on a suitable concentration-compactness argument, which can be shown to hold even though the associated functional has no sub-additive structure.
Highlights
We consider the lattice sine-Gordon equation qk(t) = V (qk+1(t) − qk(t)) − V (qk(t) − qk−1(t)) − K sin (qk(t)), k ∈ Z, (1)with a constant K > 0
The interaction potential V : R → R takes as argument the discrete strain, which is given by the difference of the positions of the atoms qk+1(t) − qk(t)
We show that a concentration-compactness result holds
Summary
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