On the Semiclassical Limit of the General Modified NLS Equation

We study the semiclassical limit of the so-called general modified nonlinear Schr¨odinger equation for initial data with Sobolev regularity, before shocks appear in the limit system. The strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case. The limiting transition from the MNLS equation to the NLS equation is also discussed.