Energy-localization in two dimensions

It is known that in continuous media, it is difficult to stabilize solitons and thus support two-dimensional energy localization. However, in the lattice context, such localization along both dimensions is possible. We have demonstrated this experimentally in the context of 2d electrical lattices.

In fairly small lattices of this type, we can stabilize two-dimensional ILMs, as shown below. The experimental results are shown at the top, for both honeycomb (a) and square lattices (b), followed by the numerical results in (c) and (d). A Floquet-analysis (panels (e) and (f)) reveals these ILMs to be dynamically stable.   

Images from PRE 88, 022912 (2013).