Abstract
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.
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