In this paper, we are concerned with arbitrarily high-order momentum-preserving and energy-preserving schemes for solving the generalized Rosenau-type equation, respectively. The derivation of the momentum-preserving schemes is made within the symplectic Runge-Kutta method, coupled with the standard Fourier pseudo-spectral method in space. Then, combined with the quadratic auxiliary variable approach and the symplectic Runge-Kutta method, together with the standard Fourier pseudo-spectral method, we present a class of high-order mass- and energy-preserving schemes for the Rosenau equation. Finally, extensive numerical tests and comparisons are also addressed to illustrate the performance of the proposed schemes.

翻译：本文分别针对广义Rosenau型方程，构造任意高阶的动量守恒格式与能量守恒格式。动量守恒格式的推导在辛Runge-Kutta方法框架内完成，并耦合了空间方向的经典Fourier拟谱方法。随后，结合二次辅助变量方法、辛Runge-Kutta方法以及经典Fourier拟谱方法，我们提出了一类用于Rosenau方程的高阶质量守恒与能量守恒格式。最后，通过大量数值实验与对比分析，验证了所提格式的性能。