Abstract
In this paper, nonlinear dynamics of higher-order rogue waves are investigated for a fifth-order nonlinear Schrodinger 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.
Highlights
A rogue wave, known as freak wave, monster wave, giant wave, episodic wave etc., is a rare, short-lived and largeamplitude local wave
Rogue waves were firstly found in the deep ocean [1], and studied in the fields of optics [2]–[4], plasmon [5], super fluids [6], capillary waves [7] and so on
A rogue wave is more precisely defined as a wave whose height is more than twice the significant wave height
Summary
A rogue wave, known as freak wave, monster wave, giant wave, episodic wave etc., is a rare, short-lived and largeamplitude local wave. In [38], the Grammian N-soliton, breather and rogue wave solutions of the cylindrical Kadomtsev-Petviashvili equation were obtained via the novel gauge transformation and long wave limit method. Yang et al studied breathers and rogue wave of the fifth-order NLS equation in the Heisenberg ferromagnetic spin chain [41]. Wang et al [44] took advantage of bilinear method and obtained the multiple lump solutions of the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation Zhao and He [45] studied the breather wave and rogue wave solutions by the modified DT and obtained the three-dimensional diagrams for the higher-order NLS equation. Carrying on the limitation procedure, we can acquire higher-order rogue wave solutions of equation (1) theoretically. It is very difficult to gain the expression of 1[4] by Maple because of complicated calculation
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