SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD

This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

Analytical study of two nonlinear Schrödinger equations via optical soliton solutions

In this study, we investigate two nonlinear Schrödinger equations (NLSEs) which point out the evolution of disturbances in dynamics. The first one is the nonlinear Heisenberg ferromagnetic spin chain equation of (2+1)-dimensional and the second one is (1+1)-dimensional cubic NLSE that govern the dynamics of modulated compressional dispersive Alfvén (CDA) envelope. The ([Formula: see text]-expansion method is adopted to carry out this target in a straightforward way. A diversity of new hyperbolic and periodic solitary wave solutions are acquired. The obtained solutions with some constraint conditions show the validity and effectiveness of the method.

Lumps and rogue waves on the periodic backgrounds for a (2 + 1)-dimensional nonlinear Schrödinger 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 [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which describes the spin dynamics for a Heisenberg ferromagnetic spin chain. Through a reduced transformation, we convert such an equation into the [Formula: see text]-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 [Formula: see text] and [Formula: see text]; the distances between two valleys of the lumps and widths of the rogue waves are affected by [Formula: see text] and [Formula: see text], where [Formula: see text] is the uniaxial crystal field anisotropy parameter, [Formula: see text] and [Formula: see text] are related to the bilinear exchange interaction, [Formula: see text] is the lattice parameter.