The current work is devoted for operating the Lie symmetry approach, to
coupled complex short pulse equation. The method reduces the coupled
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 subalgeras are solved for traveling wave solutions. Further,
with the help of similarity variable, similarity solutions and traveling
wave solutions of nonlinear ordinary differential equation, complex
soliton solutions of the coupled complex short pulse equation are
obtained which are in form of sinh, cosh, sin and cos functions.