Nonlinear dynamics of a two-axis ferromagnet on the semiaxis

Using the spectral transform on a torus, we solve the initial–boundary value problem for quasi-one-dimensional excitations in a semibounded ferromagnet, taking the exchange interaction, orthorhombic anisotropy, and magnetostatic fields into account. We used the mixed boundary conditions whose limit cases correspond to free and fully pinned spins at the sample edge. We predict and analyze new types of solitons (moving domain walls and precessing breathers), whose cores are strongly deformed near the sample boundary. At large distances from the sample surface, they take the form of typical solitons in an unbounded medium. We analyze the properties of the reflection of solitons from the sample boundary depending on the degree of spin pinning at the surface. We obtain new conservation laws that guarantee the true boundary conditions to hold when solitons reflect from the sample surface.