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由于Skjelbreia导出的确定五阶斯托克斯波的二个方程不易求解,本文将其简化为确定d/L的一个方程:f(H,T,d,d/L)=0。根据这一简化解法,发现Skjelbreia方程组的解有3种情况:存在唯一的精确解;精确解不止一个;不存在精确解(但存在满足Skjelbreia方程组方面的最佳近似解)。当精确解不止一个时,可应用变分原理的方法判别出合理的解。应用变分原理的方法还可将Skjeilbria方程组的解改进为满足无旋运动非线性波浪理论的原始数学提法方面的最佳近似解,亦即给出最优化五阶斯托克斯波。
Since Skjelbreia’s derivation of the two equations that determine the fifth-order Stokes waves is not easy to solve, we simplify it to an equation that determines d / L: f (H, T, d, d / L) = 0. According to this simplified solution, we find three kinds of solutions for Skjelbreia equations: there is only one exact solution; more than one exact solution; there is no exact solution (but there exists the best approximation solution that satisfies the Skjelbreia equation). When more than one exact solution, can be applied to the principle of variational method to identify a reasonable solution. The method of applying variational principle can also be used to improve the solution of Skjeilbria equations to the best approximate solution to the original mathematical formulation of nonlinear wave theory for non-rotating motions, ie to give an optimal fifth-order Stokes wave.