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In this paper, the generalized rational function procedure was used to produce new solitary solutions to the fractional Jaulent–Miodek hierarchy equation. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrödinger potentials. The equation is converted into a fourth-order partial differential equation using a transformation. In order, we find some solitary solutions such as soliton, rational and hyperbolic function solutions of Jaulent–Miodek hierarchy equation by the help of generalized exponential rational function procedure. Then, for some parameters, we draw three-dimensional graphics of real values of some exact solutions that we acquired by using this procedure. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of cubic–quartic NLSE with the Kerr law nonlinearity via a new sub-equation method. Considered method of undetermined coefficients is applied to obtain the introduced solutions. The outcomes are useful in describing the diffusion of optical solitons. The performance of the approach is reliable, useful and gives more new general exact solutions than the other methods. [ABSTRACT FROM AUTHOR]

In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions. Moreover, the stability property of some obtained solutions is discussed to show the ability of them for using in the model's applications. Implementation of the direct algebraic methods, the equations derived by substitution of the predicted solution are solved. It is significant to point out that new traveling wave solutions are found. The present methods are easy to employ and sufficient to determine the solutions. [ABSTRACT FROM AUTHOR]