Efficient composition conservative schemes for the Zakharov equations

Yan Zhang; Yuyang Gao; Yayun Fu; Xiaopeng Yue; Yan Zhang; Yuyang Gao; Yayun Fu; Xiaopeng Yue

doi:10.3934/math.2025379

AIMS Mathematics

2025, Volume 10, Issue 4: 8235-8251. doi: 10.3934/math.2025379

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Efficient composition conservative schemes for the Zakharov equations

1.
School of Science, Xuchang University, Xuchang 461000, China
2.
School of Mathematics, Jilin University, Changchun 130012, China

Received: 17 March 2025 Revised: 28 March 2025 Accepted: 02 April 2025 Published: 10 April 2025
MSC : 65M70

In this paper, we designed efficient conservative numerical schemes for the Zakharov system by leveraging the composition method. The core elements of our approach are as follows. First, the original Zakharov system was transformed into a Hamiltonian system through the use of the variational derivative. Then, the derived system was discretized by integrating the composition method into the Fourier pseudo-spectral method, thus obtaining fully-discrete conservative schemes. These proposed schemes are of the implicit-explicit type and can precisely preserve the discrete mass and Hamiltonian energy. To confirm the theoretical findings and demonstrate the effectiveness and conservation characteristics of our method, we conducted numerous numerical experiments.
- Zakharov equations,
- composition method,
- energy-preserving,
- Hamiltonian system
Citation: Yan Zhang, Yuyang Gao, Yayun Fu, Xiaopeng Yue. Efficient composition conservative schemes for the Zakharov equations[J]. AIMS Mathematics, 2025, 10(4): 8235-8251. doi: 10.3934/math.2025379

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Abstract

In this paper, we designed efficient conservative numerical schemes for the Zakharov system by leveraging the composition method. The core elements of our approach are as follows. First, the original Zakharov system was transformed into a Hamiltonian system through the use of the variational derivative. Then, the derived system was discretized by integrating the composition method into the Fourier pseudo-spectral method, thus obtaining fully-discrete conservative schemes. These proposed schemes are of the implicit-explicit type and can precisely preserve the discrete mass and Hamiltonian energy. To confirm the theoretical findings and demonstrate the effectiveness and conservation characteristics of our method, we conducted numerous numerical experiments.

References

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