Nonautonomous rogue waves and ‘catch’ dynamics for the combined Hirota–LPD equation with variable coefficients

•The nonautonomous rogue waves are investigated for combined Hirota-LPD equation.•We study multi-rogue wave solutions employing the generalized Darboux transformations.•There are possibilities to ‘catch’ rogue waves through manipulating nonlinear and gain functions.

We study multi-rogue wave solutions of a Schro¨dinger equation with higher-order terms employing the generalized Darboux transformation. Some properties of the nonautonomous rogue waves are investigated analytically for the combined Hirota–Lakshmanan–Porsezian–Daniel (LPD) equation. We consider the controllable behaviors of this nonautonomous rogue wave solution with the nonlinearity management function and gain/loss coefficient. It is reported that there are possibilities to ‘catch’ rogue waves through manipulating nonlinear function and gain/loss coefficient. Our approach can provide many possibilities to manipulate rogue waves and present the potential applications for the rogue wave phenomena.