Exploring certain nonlinear localized modes in an anisotropic ferromagnet with biquadratic interaction using quasi-discrete approximation

We present an analytical work on nonlinear localized modes in an anisotropic ferromagnet with added biquadratic interaction. Within the framework of quasi-discrete multiple scale approximation, it is found that the dynamics of the system is associated with the nonlinear Schrödinger (NLS) equation. The effect of anisotropic and biquadratic interactions on the nature of the linear dispersion curve is discussed. The criteria for the existence of bright and dark solitons are explored. Different classes of soliton solutions are constructed using the Hirota bilinearization method. Also, it is noted that the system and soliton parameters significantly modify the characteristics of the solitons by the inclusion of highly nonlinear invariant biquadratic interaction.