In this research article, we investigated the universal model of integrable system of modify unstable nonlinear Schrödinger equation. The mUNLSE described the disturbance of time period in slightly stable and unstable media and managed the instability of modulation wave train. We found the exact and solitary wave solutions of mUNLSE with the help of modified extended auxiliary equation mapping method. As a result, exact and solitary wave solutions in the form of elliptic functions, trigonometric functions, hyperbolic functions, bright and dark solitons, traveling wave, kink-type solitons and periodic solitary wave solution are obtained. These solutions show the power and effectiveness of this new method and two- and three-dimensional graphically with the help of computer software Mathematica. We can also solve other unstable nonlinear system of PDEs which are involved in Mathematical physics and many other branches of physical sciences with the help of this new method.

中文翻译：

---

修正的非线性非线性薛定ding动力学方程孤子解的构造。

在本文中，我们研究了修正不稳定非线性Schrödinger方程的可积系统的通用模型。mUNLSE描述了在稍微稳定和不稳定的介质中的时间周期扰动，并处理了调制波列的不稳定性。借助改进的扩展辅助方程映射方法，我们找到了mUNLSE的精确和孤波解。结果，获得了椭圆函数，三角函数，双曲函数，明暗孤子，行波，扭结型孤子和周期孤波形式的精确孤波解。这些解决方案通过计算机软件Mathematica展示了这种新方法的强大功能和有效性，并以二维和三维图形方式显示。