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).

中文翻译：

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(3+1)维Yu-Toda-Sassa-Fukuyama方程的新方法孤子解及其数值解

在本文中，我们将求解 (3 + 1) 维 Yu-Toda-Sassa-Fukuyama 方程 (YTSFE)，该方程广泛研究了流体动力学、等离子体物理学和弱色散介质中产生的孤子和非线性波的动力学。Paul-Painlevé 方法 (PPA) 首次用于获得该方程的孤子解。此外，该方程的数值解已经通过使用变分迭代法（VIM）提出。