Novel 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.

中文翻译：

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非本地媒体中二维孤子的Davey–Stewartson描述

通过将系统渐近简化为一个完全可积分的Davey–Stewartson（DS）方程组，揭示了二维（2D）非局部非线性Schrödinger（NLS）系统的新颖孤子解。这样做时，除了多尺度方案外，还采用还原摄动法来推导DS-I和DS-II系统，这取决于非局部性的强度，在此又可以将其视为对非局部性的度量。表面张力。因此，获得了两种不同的孤子解：在DS-I（弱局部性）情况下的通气和dromion解决方案，在DS-II（强局部性）情况下的整体解决方案。除了对数学的直接重要性外，由于相对非局部NLS（光学，等离子，液晶，