Bifurcation and sensitivity analysis of nonlinear waves in ferromagnetic systems with soliton solutions and applications via the conformable fractional Schrödinger equation

Abstract The nonlinear phenomena of waves in ferromagnetic systems have complex interactions with each other, which are not properly modeled by the classical theory. To overcome this shortcoming, in the present study the conformable nonlinear fractional Schrödinger equation (CNFSE) is used, whose conformable derivative retains the essential properties of classical calculus and that allows unambiguous travelling wave reductions. Using the method of ϕ expansion, dark, bright and singular soliton solutions in the exact form are constructed and the effect of fractional order κ ∈ (0, 2] on localization and dispersion is analyzed. Three-dimensional surface plots as well as contour plots show the influence of variations of parameters on wave stability and propagation. Meanwhile, bifurcation and sensitivity analyses construct features of stable and unstable equilibria, and responses to perturbations in initial conditions. The resulting analytical-computational framework provides new insights into fractional wave dynamics in corridors and ferromagnetic media, with potential applications in power transmission systems.