The current study is dedicated for operating the Lie symmetry approach, to complex short pulse equation. The method reduces the complex short pulse equation to a system of ordinary differential equations with the help of suitable similarity transformations. Consequently, these systems of nonlinear ordinary differential equations under each subalgebras are solved for exact solutions. Further, with the help of similarity variable, similarity solutions and exact solutions of nonlinear ordinary differential equation, soliton solutions of the complex short pulse equation are obtained which are in form of hyperbolic functions and trigonometric functions.

中文翻译：

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复短脉冲方程的李对称性和孤子解

当前的研究致力于对复杂的短脉冲方程进行李对称方法的操作。该方法借助于适当的相似变换将复数短脉冲方程简化为常微分方程系统。因此，求解了每个子代数下的非线性常微分方程组的精确解。此外，借助相似变量，非线性常微分方程的相似解和精确解，获得了双曲函数和三角函数形式的复短脉冲方程的孤子解。