In this study, we constructed the exact traveling and soliton solutions for unstable nonlinear Schrödinger equation (UNLSE) by a modified mathematical method. The UNLSE explains the disorder of a time period in slightly unstable and stable medium, and also accomplishes the instability for modulated carrier wave. The demonstrated soliton solutions represent to bright-dark solitons, periodic solitary wave, and traveling waves. This technique is more efficient and powerful to investigate various kinds of soliton solutions for higher order unstable nonlinear PDEs. By applying symbolic computations, the physical interpretations of soliton solutions represent by two- and three-dimensions graphical. Our obtained results may helpful in the study of nonlinear optics, fiber optics, solitonic dynamic, and various kinds of physical sciences.

中文翻译：

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非线性薛定谔动力学方程在微稳定介质中调制波列的不稳定性和时间周期的扰动

在这项研究中，我们通过改进的数学方法构建了不稳定非线性薛定谔方程（UNLSE）的精确行进和孤子解。UNLSE解释了轻微不稳定和稳定介质中时间段的无序，也完成了调制载波的不稳定性。所展示的孤子解决方案代表明暗孤子、周期性孤立波和行波。这种技术对于研究高阶不稳定非线性偏微分方程的各种孤子解更加有效和强大。通过应用符号计算，孤子解的物理解释由二维和三维图形表示。我们获得的结果可能有助于非线性光学、光纤光学、孤子动力学和各种物理科学的研究。