Forward scattering of (3 + 1)-dimensional Jimbo-Miwa (JM) equation is investigated by singular manifold method (SMM). The detected Lax pair is reduced through three parameters group method into a compatible couple of ordinary differential equations (ODEs). Three forms of symmetry variables have been discussed leading to integrable system of ODEs. Some new closed form solutions have been obtained. The three parameters group method, which is rarely used in solving PDEs, has emphasized its efficiency in creating symmetry solutions of evolution equations.

中文翻译：

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使用奇异流形和群变换方法在 (3 + 1) 维 Jimbo-Miwa 方程中进行非线性波传播的前向散射

采用奇异流形法(SMM)研究了(3+1)维Jimbo-Miwa(JM)方程的前向散射。通过三参数组方法将检测到的 Lax 对简化为一对兼容的常微分方程 (ODE)。已经讨论了三种形式的对称变量，导致 ODE 的可积系统。已经获得了一些新的封闭形式的解决方案。三参数群法在求解偏微分方程中很少使用，它强调了它在创建演化方程的对称解方面的效率。