  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.

Numerical Analysis;Numerical Analysis