Abstract
The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.
Highlights
For some decades, some researchers have focused on the rogue waves which were firstly used by Draper [1]
The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrodinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain
Rogue waves are called killer waves, freak waves, giant waves, monster waves, or extreme waves, which appeared in nautical mythology, entered the ocean waves [2,3,4], and gradually moved into other fields, such as optics [5,6,7], matter waves [8], superfluids [9], plasmas [10], atmosphere [11], and even finance [12]
Summary
Some researchers have focused on the rogue waves which were firstly used by Draper [1]. Equation (2) is generated from the deformation of the inhomogeneous Heisenberg ferromagnetic system with the prolongation structure, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain [28]. For the second-order to fourth-order nonlinear Schrodinger equations, a lot of research has been done, including the rogue waves [18, 19], soliton solutions [29,30,31], modulation instability, integrability [32,33,34], and rational solutions [35]. The paper is to obtain Nth-order rogue waves solutions for the inhomogeneous fifth-order nonlinear Schrodinger equation using the generalized DT. The nonlinear dynamics of the first-order to the third-order rogue waves are discussed with the influence of some parameters and the interesting structures are showed
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