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Soliton solutions of the (3 + 1)-dimensional Yu–Toda–Sassa–Fukuyama equation by the new approach and its numerical solutions

In this paper, we will solve the (3 + 1)-dimensional Yu–Toda–Sassa–Fukuyama equation (YTSFE) which widely investigates the dynamics of solitons and nonlinear wave arising in a fluid dynamics, plasma physics and weakly dispersive media. The Paul-Painlevé approach (PPA) is used for the first time to achieve the soliton solutions of this equation. Furthermore, the numerical solutions of this equation have been proposed by using the variational iteration method (VIM).