Two types of soliton twining behaviors for the Kraenkel-Manna-Merle system in saturated ferromagnetic materials

The main attention is focused on the twining behaviors of the solitons for the Kraenkel-Manna-Merle system, which describes the nonlinear ultra-short wave pulse motions in saturated ferromagnetic materials. Via the bilinear method, the one-soliton and two-soliton are constructed. There exist loop-like solitons between the magnetization and the external magnetic fields. Two types of soliton twining behaviors are observed when the solitons collide: (1) outer twines: the small soliton can twine along the inner tube of the big soliton; (2) inner twines: the small soliton can twine along the outer tube of the big soliton. Parameters controls on the solitons twines are also discussed.