Local structure-preserving methods for the generalized Rosenau–RLW–KdV equation with power law nonlinearity**Project supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 61672013) and the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems (Grant No. 201606).

Abstract

Local structure-preserving algorithms including multi-symplectic, local energy- and momentum-preserving schemes are proposed for the generalized Rosenau–RLW–KdV equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time–space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants.