What question did this study set out to answer?

The aim is to investigate soliton solutions within a system of coupled nonlocal nonlinear equations.

March 28, 2026Studies in Applied Mathematics0 citations

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

GKG. N. KoutsokostasNational and Kapodistrian University of Athens IMIliana MoseleyNational and Kapodistrian University of Athens GHG. HuangEast China Normal University

Key Points

The aim is to investigate soliton solutions within a system of coupled nonlocal nonlinear equations.
Analyzed a system of two coupled, two-dimensional, two-component nonlocal equations.
Utilized multiscale expansion methods to simplify the equations under specific conditions.
Considered the effects of boundary conditions and nonlinearity coefficients on the system.
Predicted the existence of weak two-dimensional solitons, including lumps and dromions.
Described various dark-antidark line soliton complexes based on model parameters.

Abstract

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.

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