A Davey–Stewartson description of two‐dimensional solitons in nonlocal media

Abstract

AbstractNovel soliton solutions of a two‐dimensional (2D) nonlocal nonlinear Schrödinger (NLS) system are revealed by asymptotically reducing the system to a completely integrable Davey–Stewartson (DS) set of equations. In so doing, the reductive perturbation method in addition to a multiple scales scheme are utilized to derive both the DS‐I and DS‐II systems, depending on the strength of the nonlocality, which in turn, may be regarded here as a measure of the surface tension. As such, two different soliton solutions are obtained: the breather and dromion solutions in the case of DS‐I (weak nonlocality), as well as lump solutions in the case of DS‐II (strong nonlocality). Besides their immediate mathematical importance, our results find a wide range of applications due the high applicability of the relative nonlocal NLS (optics, plasmas, liquid crystals, and thermal media in the strong nonlocality regime, etc.) and hence these structures can also be realized experimentally in various physical setting.