The modified Korteweg--de Vries limit of the Ablowitz--Ladik system
The modified Korteweg--de Vries limit of the Ablowitz--Ladik system
For slowly-varying initial data, solutions to the Ablowitz-Ladik system have been proven to converge to solutions of the cubic Schr\"odinger 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 …