Time–dependent coupled complex short pulse equation: Invariant analysis and complexitons

The current work is intended for investigation of complex soliton solutions and invariant analysis of time–dependent complex coupled short pulse equation with Lie symmetry analysis. In this study, invariant conditions of complex short pulse equation are addressed. Next, with the application of this invariant condition symmetries for the main equation are recovered. Finally, these symmetries are utilized to obtained the similarity solutions of the considered system. The method reduces the time–dependent equation to the system of equations in which single independent variable. Consequently, these reduced equations lead to complex soliton solutions. Further, with similarity solutions, complex soliton solutions are yielded for time–dependent complex coupled short pulse equation. These solutions are in terms of hyperbolic and exponential functions.