Existence of homoclinic travellingwaves in infinite lattices

By using critical point theory, we investigate the existence of homoclinic travelling waves in an one-dimensional infinite lattice with nearest-neighbor interactions and a on-site potential (density) f . The system is described by the infinite system of second-order differential equations: qj + f ʹ(qj(t)) =V ʹ(qj+1(t)-qj(t))-V ʹ(qj(t)-qj-1(t)), t ? R, j ? Z, where f, V ? C1(R,R). We establish three new criteria ensuring the existence of non-trivial homoclinic travelling wave solutions, for any given speed c bigger (or smaller) than some constant depending on f and V. Relevant results in the literatures are extended.