Abstract
In this research work, we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus (KE) equation with the help of modified mathematical method. We obtained the solutions in the form of dark solitons, bright solitons and combined dark-bright solitons, travelling wave and periodic wave solutions with general coefficients. In our knowledge earlier reported results of the KE equation with specific coefficients. These obtained solutions are more useful in the development of optical fibers, dynamics of solitons, dynamics of adiabatic parameters, dynamics of fluid, problems of biomedical, industrial phenomena and many other branches. All calculations show that this technique is more powerful, effective, straightforward, and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics, quantum physics, Geo physics, fluid mechanics, hydrodynamics, mathematical biology, field of engineering and many other physical sciences.