Dynamics of Partial Differential Equations

Volume 2 (2005)

Number 4

Kink-like periodic travelling waves for lattice equations with on-site and inter-site potentials

Pages: 357 – 370

DOI: https://dx.doi.org/10.4310/DPDE.2005.v2.n4.a4

Authors

Michal Fečkan (Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Bratislava, Slovakia)

Vassilis Rothos (School of Mathematical Sciences, Queen Mary, University of London, United Kingdom)

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 nonlinear equation is formulated as an advanced-delay differential 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 perturbation systems of autonomous o.d.eqns in R4. This gives the existence of generalized kink solutions with co-propagating oscillation tails.

Keywords

singular perturbations, bifurcations, travelling waves

2010 Mathematics Subject Classification

Primary 34C23, 34C25. Secondary 34C37, 35Bxx.

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Published 1 January 2005