Two‐Dimensional Solitons in a System of Two Coupled Nonlocal Gross–Pitaevskii Equations

ABSTRACT We study a system of two coupled, two‐dimensional, and two‐component nonlocal nonlinear Schrödinger (or Gross–Pitaevskii) equations. We show that, in the weakly nonlocal regime, and depending on the boundary conditions and the values of the nonlinearity coefficients, this system can be asymptotically reduced—via multiscale expansion methods—to a Kadomtsev–Petviashvili equation or to a Davey–Stewartson equation. In this way, we predict that the considered model supports weak two‐dimensional solitons, in the form of lumps or dromions, as well as a variety of dark–antidark line soliton complexes.