Bulut, Hasan; Sulaiman, Tukur A.; Baskonus, Haci Mehmet; Sandulyak, Anna A.

In this article, we employ the sine-Gordon expansion method to construct a new solitary and optical wave structures to the (1 + 1)-dimensional combined KdV–mKdV equation. Sine-Gordon expansion method is developed based on the travelling wave transformation u(x, y) = U(ξ), ξ = μ(x − ct) and the sine-Gordon equation uxx − utt = m2 sin(u). We find the travelling wave solutions to (1 + 1)-dimensional combined KdV–mKdV equation in the form of complex, hyperbolic, trigonometric and rational function. Our results show that all the travelling wave solutions we obtain are solitary and optical wave structures solutions. All the computations and graphics plot in this article are carried out with the help of Wolfram Mathematica 9.

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Sandulyak, Anna A.; Sandulyak, Alexander V.; Bulut, Hasan; Baskonus, Haci Mehmet; Polismakova, Maria N.; Sandulyak, Darya A.; Mastorakis, N; Mladenov, V; Bulucea, A

The paper demonstrates that when defining the content of ferroimpurities in the analyzed media by magnetic control based on measuring the ferroimpurities masses m, which are extracted from the media sample step-by-step, it is crucial to define a functional view of the obtained dependence m on the operation order number n. It allows receiving additional forecast data m by extrapolating this dependence. With corresponding calculations being done, it enables determining the sought total mass of ferroimpurities (including their residual mass). We consider alternate solutions of practical tasks which yield magnetic control results in case of linear and piecewise-linear views (in semi-logarithmic coordinates) of the control mass-operational characteristics.

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