Some $L^{\infty }$ solutions of the hyperbolic nonlinear Schrödinger equation and their stability

Simão Correia, Mário Figueira

Consider the hyperbolic nonlinear Schrödinger equation (HNLS) over ${\mathbb{R}}^d$ $$i{u}_t+u_{xx}-{\Delta }_{\text{y}}u+\lambda |u{|}^{\sigma }u=0.$$ We deduce the conservation laws associated wit…