The modified Korteweg–de Vries limit of the Ablowitz–Ladik system
Killip R, Ouyang Z, Vişan M, Wu L. 2025. The modified Korteweg–de Vries limit of the Ablowitz–Ladik system. Discrete and Continuous Dynamical Systems. 45(3), 821–846.
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Author
Killip, Rowan;
Ouyang, Zhimeng;
Vişan, MonicaISTA;
Wu, Lei
Abstract
For slowly-varying initial data, solutions to the Ablowitz–Ladik system have been proven to converge to solutions of the cubic Schrödinger equation. In this paper we show that in the continuum limit, solutions to the Ablowitz–Ladik system with H^1 initial data may also converge to solutions of the modified Korteweg–de Vries equation. To exhibit this new limiting behavior, it suffices that the initial data is supported near the inflection points of the dispersion relation associated with the Ablowitz–Ladik system.
Our arguments employ harmonic analysis tools, Strichartz estimates, and the conservation of mass and energy. Correspondingly, they are applicable beyond the completely integrable models of greatest interest to us.
Publishing Year
Date Published
2025-03-01
Journal Title
Discrete and Continuous Dynamical Systems
Publisher
American Institute of Mathematical Sciences
Volume
45
Issue
3
Page
821-846
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Ouyang Z, Vişan M, Wu L. The modified Korteweg–de Vries limit of the Ablowitz–Ladik system. Discrete and Continuous Dynamical Systems. 2025;45(3):821-846. doi:10.3934/dcds.2024114
Killip, R., Ouyang, Z., Vişan, M., & Wu, L. (2025). The modified Korteweg–de Vries limit of the Ablowitz–Ladik system. Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences. https://doi.org/10.3934/dcds.2024114
Killip, Rowan, Zhimeng Ouyang, Monica Vişan, and Lei Wu. “The Modified Korteweg–de Vries Limit of the Ablowitz–Ladik System.” Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences, 2025. https://doi.org/10.3934/dcds.2024114.
R. Killip, Z. Ouyang, M. Vişan, and L. Wu, “The modified Korteweg–de Vries limit of the Ablowitz–Ladik system,” Discrete and Continuous Dynamical Systems, vol. 45, no. 3. American Institute of Mathematical Sciences, pp. 821–846, 2025.
Killip R, Ouyang Z, Vişan M, Wu L. 2025. The modified Korteweg–de Vries limit of the Ablowitz–Ladik system. Discrete and Continuous Dynamical Systems. 45(3), 821–846.
Killip, Rowan, et al. “The Modified Korteweg–de Vries Limit of the Ablowitz–Ladik System.” Discrete and Continuous Dynamical Systems, vol. 45, no. 3, American Institute of Mathematical Sciences, 2025, pp. 821–46, doi:10.3934/dcds.2024114.
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