On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

This paper discusses the two-dimensional discrete monatomic Fermi--Pasta--Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.