Dispersive optical solitons of Biswas-Arshed equation with a couple of novel approaches

Purpose: The importance of efficient analytical methods in solving nonlinear partial differential equations and nonlinear optical differential equations cannot be underestimated. Because of this importance, to solve efficiently above mentioned partial differential equations, a method has been suggested to use the improved Kudryashov and a sub equation form of new extended auxiliary equation methods. In addition the modified form of method has also been given. With this choice, it has been aimed to benefit from the advantages of improved Kudryashov and sub equation of extended auxiliary equation methods at the same time without spending additional processing and time in problem solving, to obtain more solution functions and soliton types offered by the methods. Methodology: As a first step to implement the proposed method, the nonlinear ordinary differential form (NODE) of the nonlinear partial differential equation has been obtained, the algorithms of the approached methods have been presented and applied to the Biswas-Arshed problem, which is an important equation in optic. Then, the polynomial form of the problem has been obtained, the solution function of the examined problem has been formed by choosing the appropriate sets and their substitutions in the proposed solution functions. It has been checked that the solution functions satisfy the Biswas-Arshed equation and then the graphical representation of the obtained results have been given. Findings: The application of the methods has carried out successfully, and both the linear algebraic equations system, the possible solution sets and the solution functions of the main equation, have been obtained seamlessly. It has been observed that both methods can be applied successfully and effectively and more results can be obtained at the same time, without spending an additional procedure and time. It can explicitly seen from both the obtained solution functions and the graphical results that the advantages of both methods can be used at the same time and can be applied to many nonlinear problems. Originality: In summary, the originality of this work is that the Biswas-Arshed equation has not been solved with both methods separately before, and it has not been presented in a study showing that both methods can be used together.