New rational and breather solutions of a higher-order integrable nonlinear Schrödinger equation

Abstract In this letter, we investigate the general rational solutions and breather solutions of a higher-order integrable nonlinear Schrodinger (NLS) equation based on Darboux transformation (DT). The rational solutions including W-shape traveling wave solution that is not reported and rogue wave solution are constructed. Time-periodic Kuznetsov–Ma breather, space-periodic Akhmediev breather and time–space periodic breather solutions are obtained. Besides, the interaction properties of two breather solutions are also displayed through numerical simulation. The results exhibit the new dynamical properties in extended nonlinear integrable physical models.