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In this work, a new method has been applied for finding solutions to the Kundu–Mukherjee–Naskar (KMN) equation in (2[Formula: see text]+[Formula: see text]1) dimensions. These optical solutions were derived with the aid of a new method named the Exp-Function method. The method is used for solving the nonlinear governing equation, which contains high nonlinear term. This method is considered as an alternative technique for obtaining both analytical and approximate solutions for a different type of PDE with several applications in science and engineering. The efficiency of the proposed technique has been shown by a few test problems. By comparing the results obtained in this paper with other researchers it can be noticed that this method is a promising technique for finding solutions to other similar problems.

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In this paper, equations due to anion and cation distributions, electrical potential and shear stress profiles in a nanochannel are formed for 1-D electro-osmotic flow, and solved by homotopy perturbation method. Results are compared with numerical solutions

This paper reports our study on the flow characteristics and heat transfer performance of magnetohydrodynamics (MHD) nanofluid in an innovative porous, circle-shaped enclosure incorporating a Cassini oval cavity using the Darcy law. The MHD nanofluid considered in this study

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