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In this article we present a new method for construction of exact solutionsof the Landau-Lifshitz-Gilbert equation (LLG) for ferromagnetic nanowires. Themethod is based on the established relationship between the LLG and thenonlinear Schr\"odinger equation (NLS), and is aimed at resolving an oldproblem: how to produce multiple-rogue wave solutions of NLS using just theDarboux-type transformations. The solutions of this type - known as P-breathers- have been proven to exist by Dubard and Matveev, but their technique heavilyrelied on using the solutions of yet another nonlinear equation,Kadomtsev-Petviashvili I equation (KP-I), and its relationship with NLS. Wehave shown that in fact one doesn't have to use KP-I but can instead reach thesame results just with NLS solutions, but only if they are dressed via thebinary Darboux transformation. In particular, our approach allows to constructall the Dubard-Matveev P-breathers. Furthermore, the new method can lead tosome completely new, previously unknown solutions. One particular solution thatwe have constructed describes two positon-like waves, colliding with each otherand in the process producing a new, short-lived rogue wave. We called thisunusual solution (rogue wave begotten after the impact of two solitons) the"impacton".

The Landau-Lifshitz equation, the NLS, and the magnetic rogue wave as a by-product of two colliding regular "positons"