Abstract
The existence of travelling generalized kinks with oscillation tails is studied for a class of 1D lattice equations with both onsite and intersite potential. The travelling wave equation of the corresponding discrete nonlin- ear equation is formulated as an advanced{delay dieren tial equation which is reduced by a center manifold method to a 4-dimensional singular ODE with certain symmetries and with a symmetric heteroclinic structure. Bifurcations of solutions from the heteroclinic ones are investigated for the singular per- turbation systems of autonomous o.d.eqns in R4. This gives the existence of generalized kink solutions with co{propagating oscillation tails.
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