Rogue wave solutions on different periodic backgrounds for the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation

Abstract

In this paper, we will present exact rogue wave solutions on different periodic backgrounds for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, which can govern nonlinear spin dynamics of the (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. We will derive different spectral parameters and corresponding periodic eigenfunctions of Lax pair according to the nonlinearization of spectral problem. Via Darboux transformation method, first- and second-order rogue wave solutions will be derived under two different periodic seed solutions, which can be expressed by the Jacobian elliptic functions dn and cn. Meanwhile, dynamic features of these various solutions with different parameters on two kinds periodic backgrounds taking different elliptic modulus will be analytically and graphically analyzed.