Breathers and rogue waves excited by all-magnonic spin-transfer torque

In terms of Darboux transformation we investigate the dynamic process of spin wave passing through a magnetic soliton. It causes nonlinear excitations, such as Akhmediev breathers solution and Kuznetsov-Ma soliton. The former case demonstrates a spatial periodic process of a magnetic soliton forming the petal with four pieces. The spatial separation of adjacent magnetic petals increases rapidly, while one valley splits into two and the amplitude of valley increases gradually with the increasing amplitude of spin wave. The other case shows a localized process of the spin-wave background. In the limit case, we get rogue waves and clarify its formation mechanism.