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In this paper, two distinct methods are applied to look for exact traveling wave solutions of the (4+1)-dimensional nonlinear Fokas equation, namely the modified simple equation method (MSEM) and the extended simplest equation method (ESEM). Some new exact traveling wave solutions involving some parameters are obtained. The solitary wave solutions can be extracted by assigning special values of these parameters. The obtained solutions show the simplicity and efficiency of the used approaches that can be applied for nonlinear equations as well as linear ones. [ABSTRACT FROM AUTHOR]

In this paper, the modified simple equation method (MSEM) is applied to construct exact solutions of the generalized ( 2 + 1 )-dimensional nonlinear evolution equations (NLEEs) involving parameters via the ( 2 + 1 )-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation, the ( 2 + 1 )-dimensional breaking soliton equation and the ( 2 + 1 )-dimensional Bogoyavlenskii’s breaking soliton equation. The solitary wave solutions are derived from the exact solutions by assigning special values of the parameters. [ABSTRACT FROM AUTHOR]

This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented. [ABSTRACT FROM AUTHOR]