Derivation of dispersive solitons with quadrupled power law of nonlinearity using improved modified extended tanh function method

In this work, The proposed model by Kudryashov with quadruple law of nonlinearity and fourth order dispersion is studied. This model describes the propagation of a highly disperse solitons in optical fibers, which will be with a huge privilege in using in communication systems. Studying is conducted by implementing the improved modified extended tanh-function method. Various and new solutions are derived. These solutions including (dark, bright, and singular) soliton, singular periodic, rational, and exponential solutions. These solutions are important in applied physics and engineering. Furthermore, graphical simulations for some solutions are depicted to demonstrate the powerful of these solutions. This influential, consistent, and effective method can be used to solve a variety of other models in physics and other applied sciences.