描述α+β Fermi-Pasta-Ulam模型的五阶偏微分方程
The fifth-order partial differential equation for the description of the α+β Fermi-Pasta-Ulam model
摘要：
本文研究了一个新的五阶非线性偏微分方程，用于描述Fermi-Pasta-Ulam质量链中的微扰。这个五阶方程是用于描述费米-帕斯塔-乌拉姆模型的加德纳方程的扩展。我们使用的潜在的相互作用与二次和三次项相邻的群众。该方程是使用连续极限导出的。与以前的作品，我们考虑到高阶项的泰勒级数展开。我们使用Painlevé方法研究方程。我们证明了该方程不能通过Painlevé检验，也不能用逆散射变换积分。本文用逻辑函数法和罗朗展开法求五阶方程的行波解。本文用拟谱方法对波动过程进行数值模拟，用方程描述。
英文摘要：
We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi--Pasta--Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth--order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.
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