Nonlinear localized waves for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

We focus on the spin dynamics of the nonlinear localized waves for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation. Based on the technique for the nonlinearization of spectral problem, we derive the values of the spectral parameter and periodic eigenfunction of the Lax pair associated with dn which is the Jacobian elliptic function of the third kind. According to the Darboux transformation, we take the seed solutions expressed by the Jacobian elliptic function and construct the semirational solutions. Such solutions are used for describing the eye-shaped lumps and line rogue waves on the dn-periodic backgrounds. Besides, the lump and mixed lump-soliton solutions are deduced through the semirational solutions.

Automated summary

This study focuses on the spin dynamics of nonlinear localized waves in the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation. By employing the technique for the nonlinearization of spectral problem, the values of spectral parameters and periodic eigenfunctions are derived, leading to the construction of semirational solutions to describe various phenomena such as eye-shaped lumps and line rogue waves on dn-periodic backgrounds. Furthermore, lump and mixed lump-soliton solutions are deduced through these semirational solutions.