Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions
The authors study a matrix Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonvanishing boundary conditions at infinity. Different soliton solutions are sought in a uniaxial ferromagnetic nanowire. The authors introduce an affine transformation which converts the boundary functions into constants, and thus obtain asymptotic Lax pairs. Analytic properties of the scattering matrix are obtained using a spectral analysis. The dynamical behavior of soliton solutions are also studied with reflectionless potentials. Finally, characteristics of the soliton solutions are analyzed graphically, and based on the analytic solutions, the authors propose a method for controlling nonlinear phenomena related to the dynamics of the soliton waves and breather waves.
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