Linearly implicit energy-preserving Fourier pseudospectral schemes for the complex modified Korteweg-de Vries equation




mass, energy, invariant energy quadratization method, Fourier pseudo-spectral method, complex modified Korteweg-de Vries equation


We propose two linearly implicit energy-preserving schemes for the complex modified Korteweg–de Vries equation, based on the invariant energy quadratization method. First, a new variable is introduced and a new Hamiltonian system is constructed for this equation. Then the Fourier pseudospectral method is used for the space discretization and the Crank–Nicolson leap-frog schemes for the time discretization. The proposed schemes are linearly implicit, which is only needed to solve a linear system at each time step. The fully discrete schemes can be shown to conserve both mass and energy in the discrete setting. Some numerical examples are also presented to validate the effectiveness of the proposed schemes.



Author Biographies

J. L. Yan, Wuyi University


Department of Mathematics and Computer, Wuyi University, Wu Yi Shan 354300, China.



L. H. Zheng, No.1 middle school of Nanping

Department of Information and Computer Technology, No.1 middle school of Nanping, Napping, 35300, China.


L. Zhu, Jiangsu University of Science and Technology

Department of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, 212003, China.

F. Q. Lu, Changzhou Institute of Technology

Changzhou Institute of Technology, Changzhou 213032, China.





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