Electrochemical degradation of such dyes as methylene blue (BM-ylene) and methyl blue (BM-yl) was investigated using UV-Vis spectrophotometry, in order to be removed from the solutions, leading to discoloration of wastewater obtained under simulated laboratory conditions. The electrochemical degradation in the presence of 2 4 SO  ions, as well as in the presence of Clions were compared for the synthetic waters containing BM-ylene and BM-yl. The results showed that the fastest degradation and discoloration of the BM-yl solution containing Clions was achieved, with a high value for its color removal (CR) of 89.7% obtained after 10 min.

This paper presents the functional expansion approach as a generalized method for finding traveling wave solutions of various nonlinear partial differential equations. The approach can be seen as a combination of the Kudryashov and G′/G solving methods. It allowed the extension of the first method to the use of second order auxiliary equations, and, at the same time, it allowed non-standard G′/G-solutions to be generated. The functional expansion is illustrated here on the Dodd–Bullough–Mikhailov model, using a linear second order ordinary differential equation as an auxiliary equation.

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