A discrete phi^4 system without Peierls-Nabarro barrier

Details A discrete phi^4 system without Peierls-Nabarro barrier A discrete phi^4 system without Peierls-Nabarro barrier

1997-03-17

arxiv.org/abs/patt-sol/9703005v1

Nonlinearity, 10 (1997) 1615-1625

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, LaTeX, 8 postscript figures

Scientific paper

10.1088/0951-7715/10/6/010

A discrete phi^4 system is proposed which preserves the topological lower bound on the kink energy. Existence of static kink solutions saturating this lower bound and occupying any position relative to the lattice is proved. Consequently, kinks of the model experience no Peierls-Nabarro barrier, and can move freely through the lattice without being pinned. Numerical simulations reveal that kink dynamics in this system is significantly less dissipative than that of the conventional discrete phi^4 system, so that even on extremely coarse lattices the kink behaves much like its continuum counterpart. It is argued, therefore, that this is a natural discretization for the purpose of numerically studying soliton dynamics in the continuum phi^4 model.

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