Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation

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. Unlike the momentum-preserving scheme, the energy-preserving one relies on the use of the quadratic auxiliary variable approach and the symplectic Runge-Kutta method, as well as the standard Fourier pseudo-spectral method. Extensive numerical tests and comparisons are also addressed to illustrate the performance of the proposed schemes.