Complex nonlinearities of rogue waves in generalized inhomogeneous higher-order nonlinear Schrodinger equation

In this paper, the Nth-order rogue waves are investigated for an inhomogeneous higher-order nonlinear Schrodinger equation. Based on the Heisenberg ferromagnetic spin system, the higher-order nonlinear Schrodinger equation is generated. The generalized Darboux transformation is constructed by the Darboux matrix. The solutions of the Nth-order rogue waves are given in terms of a recursive formula. There are complex nonlinear phenomena in the rogue waves, add the first-order to the fourth-order rogue waves are discussed in some figures obtained by analytical solutions. It is shown that the general Nth-order rogue waves contain free parameters. The free parameters play a crucial role to affect the dynamic distributions of the rogue waves. The results obtained in this paper will be useful to understand the generation mechanism of the rogue wave.