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This article presents soliton solutions to a generalized nonlinear Fokas-Lenells equation via the Sine-Gordon expansion method. To uncover the clear picture of the gained solutions, the two and three-dimensional figures for the solutions are given. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

In this work, we construct multi-soliton solutions of the ( 2 + 1 ) -dimensional breaking soliton equation with variable coefficients by using the generalized unified method. We employ this method to obtain double- and triple-soliton solutions. Furthermore, we study the nonlinear interactions between these solutions in a graded-index waveguide. The physical insight and the movement role of the waves are discussed and analyzed graphically for different choices of the arbitrary functions in the obtained solutions. The interactions between the solitons are elastic whether the coefficients of the equation are constants or variables. [ABSTRACT FROM AUTHOR]

The present paper explores the generalized third-order nonlinear Schrödinger (GTONLS) equation which is used to model ultra-short pulses in optical fibers. The analysis is carried out systematically by adopting a complex transformation for reducing the GTONLS equation to a couple of nonlinear ordinary differential equations (NLODEs) with specific conditions such that the resulting NLODEs can be solved through the use of well-designed techniques such as the exp a -function and unified methods. As an outcome, different wave structures including dark and bright solitons as well as Jacobi elliptic solutions to the model are formally constructed. [ABSTRACT FROM AUTHOR]

This article offers a well-organized and novel algorithm for solving time-fractional Fornberg–Whitham, Klein–Gordon equation and biological population models occurring from physics and engineering. The Elzaki (E)-transformation and decomposition process are combined in this algorithm. To evaluate the numerical outcomes of fractional-order partial differential equations, the E -transform decomposition method is generated in series form and nonlinearity terms are decayed. To demonstrate the feasibility of the proposed approach, numerical algorithms and examples are illustrated via graphs and tables. Moreover, it is viewed that the solutions of the new methodology are in strong correlation with the exact findings. Numerical simulations were carried out to ensure that the proposed methods are precise, as shown by the exact solutions resolving complex nonlinear problems. [ABSTRACT FROM AUTHOR]