Solitary waves on a two-dimensional lattice

In this paper we analyse the solitary wave structures observed in a two-dimensional lattice using the methods detailed in an earlier paper [1]. In particular we provide a prediction of the form of anisotropy of plane waves that was first noted in numerical calculations. All methods describe the effect of anisotropy on the width of solitary waves, but only one of the methods analysed is capable of describing the effect of anisotropy on the height. A difference in two forms of continuum approximation is noted that does not occur in simpler lattices, i.e. in one-dimensional lattices the methods give the same results, whereas in the lattice studied here, one is shown to be more accurate than the other.