Dispersive propagation of optical solitions and solitary wave solutions of Kundu-Eckhaus dynamical equation via modified mathematical method

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.

Automated summary

In this research work, we obtained the optical soliton solutions of the nonlinear complex Kundu-Eckhaus (KE) equation using a modified mathematical method. These solutions include dark solitons, bright solitons, combined dark-bright solitons, travelling wave solutions, and periodic wave solutions with general coefficients. These solutions are useful in various fields such as optical fiber development, soliton dynamics, adiabatic parameter dynamics, fluid dynamics, biomedical problems, and industrial phenomena. The technique used in this research proves to be powerful, effective, and fruitful for studying other higher-order nonlinear complex PDEs in fields like mathematical physics, quantum physics, geophysics, fluid mechanics, mathematical biology, engineering, and other physical sciences.