In this paper, the perturbed nonlinear Schrödinger equation with dual-power law of nonlinearity is studied by adopting four mathematical methods namely the Modified Kudryashov method, the extended Tanh–Coth method, the modified simple equation method and soliton ansatz method. As a results, a set of various types of solitons that contains dark, singular, dark–singular, bright optical solitons and other form of optical soliton solutions are obtained. Firstly, we solve the perturbed nonlinear Schrödinger equation by considering the dual power law parameter using the first three integration methods and secondly we set this parameter equal to one in order, to solve the problem with the fourth method. The used methods in this paper present various applications in fields of nonlinear wave equations. Comparing our new results with well-known in literature are also given. Moreover, the graphical representations of the modulus of some optical soliton solutions and their 2-D profile are also depicted.

中文翻译：

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具有非线性双幂律的扰动非线性薛定谔方程的精确光孤子

本文采用修正Kudryashov法、扩展Tanh-Coth法、修正简单方程法和孤子Ansatz法四种数学方法研究了具有非线性双幂律的扰动非线性薛定谔方程。结果，获得了一组包含暗、奇异、暗-奇异、亮光学孤子和其他形式的光学孤子解的各种类型的孤子。首先，我们使用前三种积分方法通过考虑对偶幂律参数来求解扰动非线性薛定谔方程，其次我们将该参数设置为等于1，以解决第四种方法的问题。本文中使用的方法在非线性波动方程领域具有多种应用。还给出了将我们的新结果与文献中众所周知的结果进行比较。此外，还描绘了一些光学孤子解决方案的模量及其二维轮廓的图形表示。