Nonlinear Dynamics of Rogue Waves in a Fifth-Order Nonlinear Schrödinger Equation

In this paper, nonlinear dynamics of higher-order rogue waves are investigated for a fifth-order nonlinear Schrödinger equation, which can depict the Heisenberg ferromagnetic spin chain. A generalized Darboux transformation is constructed based on the Lax pair. Higher-order rogue waves solutions are given in terms of a recursive formula. Using numerical simulation, the first-order to the third-order rogue waves are displayed on the basis of some free parameters, which play a crucial role in affecting the distribution of rogue waves. The results obtained should be useful in understanding the generation mechanism of rogue waves.