A Conformal Generalized Multi-Symplectic Fourier Pseudo-Spectral Algorithm for Damping eKdV-Burgers Equations

LI Qian; WANG Guixia; WANG Yichen

doi:10.21656/1000-0887.450263

Volume 46 Issue 11

Nov. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(11): 1464-1479

LI Qian, WANG Guixia, WANG Yichen. A Conformal Generalized Multi-Symplectic Fourier Pseudo-Spectral Algorithm for Damping eKdV-Burgers Equations[J]. Applied Mathematics and Mechanics, 2025, 46(11): 1464-1479. doi: 10.21656/1000-0887.450263

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A Conformal Generalized Multi-Symplectic Fourier Pseudo-Spectral Algorithm for Damping eKdV-Burgers Equations

doi: 10.21656/1000-0887.450263

LI Qian¹,
WANG Guixia^{1,2,3
,
,},
WANG Yichen¹

1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China;
2. Center for Applied Mathematics Science, Inner Mongolia, Hohhot 010022, P.R.China;
3. Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, Hohhot 010022, P.R.China

Funds:

The National Science Foundation of China(62161045)

Received Date: 2024-09-29
Rev Recd Date: 2024-12-24

Available Online: 2025-12-05

Abstract

Abstract

Based on the conformal generalized multi-symplectic theory for Hamiltonian systems, a class of conformal generalized multi-symplectic pseudo-spectral algorithms for damping eKdV-Burgers the equations were studied. Firstly, through introduction of intermediate variables, the equation was transformed into a conformal generalized multi-symplectic Hamiltonian system satisfying local conservation, and the Strang splitting method was used to split it into a conservative subsystem and a dissipative subsystem. Furthermore, the Fourier pseudo-spectral method was applied spatially and the hidden midpoint method applied temporally to discretize the system to obtain the conformal generalized multi-symplectic Fourier pseudo-spectral scheme, which meets the global conformal mass conservation law and the momentum conservation law under the periodic boundary conditions. Numerical examples show that, the algorithm is effective and can maintain the mass and momentum decay characteristics of the system.
- dissipative term,
- shallow water effect,
- eKdV-Burgers equation,
- conformal generalized multi-symplectic,
- Fourier pseudo-spectral method,
- Strang split

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References

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