Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

Abstract EN

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.