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arXiv · 2206.02720

Continuum limit for the Ablowitz--Ladik system

Rowan Killip·Zhimeng Ouyang·Monica Visan·Lei Wu
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Abstract

We show that solutions to the Ablowitz--Ladik system converge to solutions of the cubic nonlinear Schr\"odinger 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 Schr\"odinger equations.

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Rowan Killip, Zhimeng Ouyang, Monica Visan, Lei Wu. 2022-06-06. Continuum limit for the Ablowitz--Ladik system. https://doi.org/10.1088/1361-6544/acd978

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