In this paper, we will investigate a famous model of nonlinear sciences namely (2 + 1)-dimensional nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) model for the evaluation of...

Conserved quantities along with Painlevé analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model

https://iopscience.iop.org/article/10.1088/1572-9494/ab6181/pdf

Investigation of soliton solutions with different wave structures to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation

https://scholarworks.utrgv.edu/cgi/viewcontent.cgi?article=1028&context=mss_fac

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

We consider a nonlinear Schrodinger type equation in (2+1) dimensions. The proposed equation describes the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. We first construct three families of exact periodic solutions expressed in terms of Jacobi’s elliptic functions cn,  sn and dn. We second consider the limit where the elliptic modulus approaches 1 to obtain bright and dark soliton solutions. Furthermore, we find a new type of soliton-like solution, illustrating the potentially rich set of wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation. Parametric conditions for the existence and uniqueness of exact solutions are presented. The derived structures of the obtained solutions offer a rich platform to study the nonlinear spin dynamics in magnetic materials.

New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

This study uses two mathematical approaches in constructing dark, bright, kink-type and singular soliton solutions to the Heisenberg ferromagnetic spin chain equation. The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation describes nonlinear dynamics of magnets. The acquired results in this study may help in explaining some physical meanings of some nonlinear physical models arising in electromagnetic waves. For instance, the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic cotangent arises in the Langevin function for magnetic polarization. The 2-, 3-dimensional and the contour plots of all the acquired solutions are presented.

Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation

We investigate the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic (FM) spin chains with bilinear and anisotropic interactions in the semiclassical limit using the coherent state ansatz combined with the Holstein–Primakoff (HP) bosonic representation of spin operators. In the continuum limit the dynamics is found to be governed by a new integrable nonlinear Schrodinger type equation in (2+1) dimensions. The integrability of the equation is studied by constructing Lax pair of operators. The multisoliton solution is generated through the Darboux transformation. We also propose a model representing the (2+1)-dimensional inhomogeneous Heisenberg FM spin chain and the effect of inhomogeneity is understood by performing a perturbation analysis. Finally, the modulation instability aspects are discussed via analytic solutions and graphical illustrations.

https://iopscience.iop.org/article/10.1088/0031-8949/89/6/065204/pdf

An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations

Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions in (2 + 1) dimensions

We study the dynamics of (2+1) dimensional ferromagnetic spin chain with bilinear and biquadratic interactions by using Holstein–Primakoff (HP) representation and the coherent state ansatz. The dynamical equations of motion are obtained by using long wavelength approximation. The sine–cosine function method is used to study the complete nonlinear excitation and the effect of the different types of interactions is investigated graphically.

Dromions in (2+1) dimensional ferromagnetic spin chain with bilinear and biquadratic interactions

Soliton excitation in a one-dimensional antiferromagnet with Dzyaloshinski?Moriya interaction has been studied using the Holstein?Primakoff representation, the coherent-state ansatz and the time-dependent variational principle. The dynamics is found to be governed by a set of coupled nonlinear partial differential equations. Employing the sine?cosine function method with minimal algebra, we analyse the effect of inhomogeneity in terms of soliton under perturbation and it is found that inhomogeneity causes splitting in soliton and hence a disorder in the system.

https://iopscience.iop.org/article/10.1088/0031-8949/88/06/065012/pdf

Nonlinear dynamics of inhomogeneous antiferromagnetic system with Dzyaloshinski?Moriya interactions

We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.

C. Christal Vasanthi

Papers

An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations

Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions in (2 + 1) dimensions

Dromions in (2+1) dimensional ferromagnetic spin chain with bilinear and biquadratic interactions

Nonlinear dynamics of inhomogeneous antiferromagnetic system with Dzyaloshinski?Moriya interactions

A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities