Efficient structure-preserving algorithms for Zakharov–Rubenchik equation

Purpose This study aims to develop efficient structure-preserving algorithms that can enhance the computation efficiency and conserve the physical properties in the simulation of nonlinear Zakharov–Rubenchik equation. Design/methodology/approach Six efficient structure-preserving algorithms are developed by combing the Crank–Nicolson (C-N) scheme with the extrapolation method, and the numerical computation is implemented by solving a linear system. Findings The proposed algorithms can enhance the computation efficiency and satisfy some physical properties for almost all cases tested, especially for the Alfvén wave with small amplitudes. Research limitations/implications The proposed algorithm can enhance the computation efficiency and satisfy some physical properties for different problems. It can only attain second-order accuracy in time. Practical implications The proposed algorithms are simple, efficient and can conserve discrete properties of the original system. The numerical computations only need to solve a linear system. Originality/value The paper developed six efficient structure-preserving algorithms by combing the C-N scheme with the extrapolation method, and the numerical computation is implemented by solving a linear system at each time step. The proposed methods developed in this work can be applied to simulate a wide range of other nonlinear problems.