Explicit solutions for a nonlinear model on the honeycomb and triangular lattices

We study a simple nonlinear model defined on the honeycomb and triangular lattices. propose bilinearization scheme for field equations demonstrate that resulting system is closely related to well-studied integrable models, such as Hirota bilinear difference equation Ablowitz-Ladik system. This result used derive two sets of explicit solutions: N-soliton solutions ones constructed Toeplitz determinants.