On the Wave Solutions of (2+1)-Dimensional Time-Fractional Zoomeron Equation

Year 2020, Volume: 8 Issue: 2, 410 - 418, 27.10.2020

Hajar Ismael , Hasan Bulut

Abstract

In this manuscript, we have applied the sine-Gordon expansion method and the Bernoulli sub-equation method to seek the traveling wave solutions of the (2+1)-dimensional time-fractional partial Zoomeron equation. The exact solutions of the Zoomeron equation that are obtained by the sine-Gordon method are plotted in 3D figures, as well as the effects of the fractional derivative $\alpha $ are illustrated in 2D figures, while the exact solutions of the Zoomeron equation that are obtained by the Bernoulli sub-equation method are plotted in 3D figures and contour plot. Bright solutions, kink soliton, singular soliton solution, and complex solutions to the studied equation are constructed. Also, different values of the fractional parameter $\alpha $ are tested to study the effect of the parameter. We conclude that these methods are sufficient for seeking the exact solutions.

Keywords

time fractional, sine-Gordon method, Bernoulli sub-equation method, Zoomeron equation

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