Bright N-solitons for the intermediate nonlinear Schr\"{o}dinger equation

A previously unknown bright N-soliton solution for an intermediate nonlinear Schr\"{o}dinger equation of focusing type is presented. This equation is constructed as a reduction of an integrable system related to a Sato equation of a 2-component KP hierarchy for certain differential--difference dispersion relations. Bright soliton solutions are obtained in the form of double Wronskian determinants.