Analytic studies on a generalized inhomogeneous higher-order nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain

• Bilinear forms, analytic soliton solutions are derived via the Hirota method.
• Effects of the linear inhomogeneities on the soliton are investigated.
• We see the existence of explode–decay soliton.
• We find the interaction between two solitons follows the attraction–repulsion process.

For the dynamics of spins in an inhomogeneous classical continuum biquadratic Heisenberg ferromagnetic spin chain with the deformation of the inhomogeneous Heisenberg ferromagnetic spin system through a space curve formalism, we work on the behavior of solitons described by a generalized inhomogeneous higher-order nonlinear Schrödinger equation. Upon the introduction of an auxiliary function, bilinear forms, analytic one- and two-soliton solutions are derived via the Hirota method. We find that the inhomogeneous parameters can affect the amplitude of the soliton, and also see the existence of explode–decay soliton. Asymptotic analysis is carried out on the two-soliton solutions. Effects of the linear inhomogeneities on the one and two solitons are investigated graphically and analytically. Soliton amplitude and peak position are related to the inhomogeneous coefficients of the equation. Interaction between two solitons follows the attraction–repulsion process.