Issue |
EPL
Volume 146, Number 3, May 2024
|
|
---|---|---|
Article Number | 32002 | |
Number of page(s) | 7 | |
Section | Mathematical and interdisciplinary physics | |
DOI | https://doi.org/10.1209/0295-5075/ad3a10 | |
Published online | 14 May 2024 |
Numerical calculation of N-periodic wave solutions of the negative-order Korteweg-de Vries equations
1 School of Mathematics, North University of China - Taiyuan, Shanxi 030051, PRC
2 School of Mathematics, China University of Mining and Technology - Xuzhou, Jiangsu, 221116, PRC
Received: 8 February 2024
Accepted: 2 April 2024
In this paper, the N-periodic wave solutions of the negative-order Korteweg-de Vries equations are presented, which can be used to describe wave phenomena in the water waves and plasma waves. Combining the bilinear Bäcklund transformation with the Riemann-theta function, the N-periodic wave solutions can be obtained. Employing the parity of the bilinear forms for the Bäcklund transformation, the complexity of the calculation can be reduced. The difficulty of solving N-periodic wave solutions can be transformed into solving least square problems. The Gauss-Newton numerical algorithm is employed to solve this kind of problem. Furthermore, the characteristic lines are used to analyze quantitatively the quasi-periodic solutions. The characteristic line analysis method is specifically demonstrated in the case of N = 3. Some examples of numerical simulations for the 3-periodic and 4-periodic waves are presented. It is proved that this method can be further extended to the N-periodic wave solutions.
© 2024 EPLA
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