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Open AccessArticle
mKdV Equation on Time Scales: Darboux Transformation and N-Soliton Solutions
by
Baojian Jin
Baojian Jin
Yong Fang
Yong Fang
Dr. Yong Fang graduated from the Institute of Oceanography,
Chinese Academy of Sciences, in June in [...]
Dr. Yong Fang graduated from the Institute of Oceanography,
Chinese Academy of Sciences, in June 2014, majoring in physical oceanography.
also obtaining a doctor's degree in science. In July of the same year, he joined
the State Key Laboratory of Tropical Marine Environment of the South China Sea
Institute of Oceanography, Chinese Academy of Sciences. In July 2018, he
transferred to the Shandong University of Science and Technology. In September
2020, he received funding from the Hong Kong Qiu Cha Foundation to visit and
exchange ideas at the Education University of Hong Kong. He is currently the
Academic Vice Dean of the School of Mathematics and Systems Science (Alibaba
Cloud Big Data College) at the Shandong University of Science and Technology.
and
Xue Sang
Xue Sang
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(9), 578; https://doi.org/10.3390/axioms13090578 (registering DOI)
Submission received: 17 June 2024
/
Revised: 21 August 2024
/
Accepted: 23 August 2024
/
Published: 25 August 2024
Abstract
In this paper, the spectral problem of the mKdV equation satisfying the compatibility condition on time scales is directly constructed. By using the zero-curvature equation on time scales, the mKdV equation on time scales is obtained. When and , the equation degenerates to the classical mKdV equation. Then, the single-soliton, two-soliton, and N-soliton solutions of the mKdV equation under the zero boundary condition on time scales are presented via employing the Darboux transformation (DT). Particularly, we obtain the corresponding single-soliton solutions expressed using the Cayley exponential function on four different time scales (, , q-discrete, ).
Share and Cite
MDPI and ACS Style
Jin, B.; Fang, Y.; Sang, X.
mKdV Equation on Time Scales: Darboux Transformation and N-Soliton Solutions. Axioms 2024, 13, 578.
https://doi.org/10.3390/axioms13090578
AMA Style
Jin B, Fang Y, Sang X.
mKdV Equation on Time Scales: Darboux Transformation and N-Soliton Solutions. Axioms. 2024; 13(9):578.
https://doi.org/10.3390/axioms13090578
Chicago/Turabian Style
Jin, Baojian, Yong Fang, and Xue Sang.
2024. "mKdV Equation on Time Scales: Darboux Transformation and N-Soliton Solutions" Axioms 13, no. 9: 578.
https://doi.org/10.3390/axioms13090578
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