Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity

We construct certain higher order smooth positon and breather solutions of an extended nonlinear Schrödinger equation with the cubic quartic nonlinearity. utilize generalized Darboux transformation method to aforementioned solutions. The three well-known equations, namely equation, Hirota are sub-cases considered equation. which we more general. analyze how constituent equations get modified by dispersion terms. Our results show that width direction breather-positon highly sensitive higher-order effects. Further, carry out asymptotic analysis predict behaviour positons. observe during collision positons exhibit a time-dependent phase shift. also present exact expression shift Finally, this is directly proportional parameters.