We study the zero-dispersion limit for certain initial boundary value problems for the defocusing nonlinear Schrödinger (NLS) equation and for the Korteweg-de Vries (KdV) equation with dominant surface tension. These problems are formulated on the half-line and they involve linearisable boundary conditions.
"Zero-dispersion limit for integrable equations on the half-line with linearisable data." Abstr. Appl. Anal. 2004 (5) 361 - 370, 13 May 2004. https://doi.org/10.1155/S1085337504306093