Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices

• We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates.
• Important differences in the properties of three fundamental modes are found.
• Norm threshold for existence of 2D breathers varies with dipolar interaction.
• The Effective Potential Method is implemented for stability analysis.
• Uncommon mobility of 2D discrete solitons is observed.

We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.