Lumps and rogue waves on the periodic backgrounds for a (2+1)-dimensional nonlinear Schrodinger equation in a Heisenberg ferromagnetic spin chain

Spin excitations for the magnetic materials are used in the nonlinear signal processing devices and microwave communication systems. Under consideration in this paper is a (2 + 1)-dimensional nonlinear Schrodinger (NLS) equation which describes the spin dynamics for a Heisenberg ferromagnetic spin chain. Through a reduced transformation, we convert such an equation into the (1 + 1)-dimensional focusing NLS equation. Via the rogue-periodic solutions associated with two types of the Lie symmetry transformations of the NLS equation, we present the lump- and rogue-periodic solutions. Besides, the lump and mixed lump-soliton solutions are deduced. We graphically investigate the lump- and rogue-periodic waves and find that the amplitudes of the lumps and rogue waves are negatively related to vertical bar A vertical bar and vertical bar gamma vertical bar; the distances between two valleys of the lumps and widths of the rogue waves are affected by J and J(1), where A is the uniaxial crystal field anisotropy parameter, J and J(1) are related to the bilinear exchange interaction, gamma is the lattice parameter.