THE SMOOTH SOLUTIONS OF A CLASS OF COUPLED KDV EQUATIONS

Boling Guo; Qi Guo

doi:10.11948/20220477

2024 Volume 14 Issue 5

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Boling Guo, Qi Guo. THE SMOOTH SOLUTIONS OF A CLASS OF COUPLED KDV EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2505-2522. doi: 10.11948/20220477

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Boling Guo, Qi Guo. THE SMOOTH SOLUTIONS OF A CLASS OF COUPLED KDV EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2505-2522. doi: 10.11948/20220477

THE SMOOTH SOLUTIONS OF A CLASS OF COUPLED KDV EQUATIONS

Boling Guo^1,,
Qi Guo^2, ,

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
2.
The Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Author Bio: Email: gbl@iapcm.ac.cn(B. Guo)
Corresponding author: Email: guoqi20@gscaep.ac.cn(Q. Guo)

Abstract

Abstract

This paper is devoted to the study of the periodic initial boundary value problem and Cauchy problem for the coupled KdV equations. By the Galerkin method and sequential approximation, we get a series of a priori estimates and establish the existence of classical local solution to the periodic problem for the system. Then we obtain the existence and uniqueness of global smooth solution when the coefficients of the system satisfy certain conditions by energy method, conserved quantities and nonconservative quantity $ I(u, v) $.
- KdV equations /
- periodic solutions /
- conserved quantities
MSC: 35Q53, 35B45

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References

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