2014
DOI: 10.1088/0256-307x/31/6/060201
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Rogue Wave Solutions for the Heisenberg Ferromagnet Equations

Abstract: Darboux transformation of the Heisenberg ferromagnet equation is constructed by the Darboux matrix method. In application, the rogue wave solutions of the Heisenberg ferromagnet equation are obtained. In particular, rogue waves are discussed and illustrated.

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Cited by 13 publications
(6 citation statements)
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“…Next, we construct a single Darboux transformation for the generalized Landau-Lifshitz equation with a self-consistent potential [16]. To do this, consider the following transformation of the solutions of the system (3)-( 4)…”
Section: The Darboux Transformationmentioning
confidence: 99%
“…Next, we construct a single Darboux transformation for the generalized Landau-Lifshitz equation with a self-consistent potential [16]. To do this, consider the following transformation of the solutions of the system (3)-( 4)…”
Section: The Darboux Transformationmentioning
confidence: 99%
“…This 'seed' spin is a static field (independent of t) with energy density k 4 0 2 . Recently, Darboux transformation has been constructed starting with a more general seed solution [35,36] for which (20) arises as a special case. A comparative study between classical HF model and the NLSE, in the context of breather (rogue) excitations has also been done recently [37], wherein the space curve formalism has been employed to obtain the curvature and torsion associated with NLSE breather solutions.…”
Section: Exact Recurrence In Classical Hf Spin Chainmentioning
confidence: 99%
“…The whole paper is organized as follows. In section 2, we adopt a hodograph transformation to transform the 2SP equation ( 2) to another nonlinear partial differ ential equation, which is a Lax integrable system belonging to the Heisenberg ferromagnet (HF) hierarchy [44,60]. In section 3, we define a Darboux transformation in terms of the Darboux matrix, and then provide a detailed proof for the Darboux transformation and its quasideterminant representation of the N-fold case.…”
Section: Introductionmentioning
confidence: 99%