The search for soliton solutions of nonlocal Schrödinger equations in the presence of nonlinear effects has received special interest in the last few decades. In the present paper, a weakly nonlocal Schrödinger equation (WNSE) involving the parabolic law nonlinearity is considered and as a success, its soliton solutions including bright and dark solitons are constructed. Such a key goal is formally carried out using a series of efficient approaches such as Kudryashov and exponential methods (Their new versions). The results presented in this paper are of a significant role to describe the propagation of soliton waves in the weakly nonlocal parabolic law medium.

在最近的几十年中，在存在非线性效应的情况下寻找非局部Schrödinger方程的孤子解引起了人们的特别兴趣。在本文中，考虑了涉及抛物线非线性的弱非局部薛定ding方程（WNSE），并成功地构造了它的包括亮和暗孤子的孤子解。使用一系列有效方法（例如Kudryashov和指数方法）（其新版本）正式实现了这一关键目标。本文介绍的结果对于描述孤子波在弱非局部抛物线定律介质中的传播具有重要作用。