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Continuum limit for the Ablowitz–Ladik system
Abstract We show that solutions to the Ablowitz–Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely L 2 initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schrödinger equations.
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- PAR ID:
- 10450479
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 36
- Issue:
- 7
- ISSN:
- 0951-7715
- Page Range / eLocation ID:
- 3751 to 3775
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-6544/acd978
