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I.V. Barashenkov, O.F. Oxtoby, and D.E. Pelinovsky

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Translationally invariant discrete kinks from one-dimensional maps

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Phys. Rev. E 92, 035602(R) (2005)

**Abstract:**

For most discretisations of the phi-4 theory, the stationary kink can only be centered
either on a lattice site or midway between two adjacent sites. We search for exceptional
discretisations which allow stationary kinks to be centered anywhere between the sites. We
show that this translational invariance of the kink implies the existence of an underlying one-dimensional
map phi_{n+1} = F(phi_{n}). A simple algorithm based on this observation generates three different
families of exceptional discretisations.

**Keywords**:

DISCRETE PHI-4 EQUATION, STATIONARY KINKS, DISCRETE MAPS,
EXISTENCE PROBLEM, STOKES CONSTANTS