On integrability of the inhomogeneous Heisenberg ferromagnet model: Examination of a new test

It is established that, in steady circulation-preserving hydrodynamic motions with velocity q = qt subject to either of the geometric constraints t · curl t = 0 or div t = 0, the geodesic unit tangent t-field is constrained by privileged Heisenberg spin-type equations. In the case div t = 0, remarkably, the integrable Heisenberg spin equation related to the solitonic nonlinear Schrödinger equation is obtained. Corresponding results hold "mutatis mutandis" in magneto-hydrostatics.

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“…It has been investigated extensively when µ is linear in s, in which case it is integrable [16][17][18].…”

Section: Geodesic Motionsmentioning

confidence: 99%

On Geodesic Hydrodynamic Motions. Heisenberg Spin Connections

Rogers

Schief

2000

Journal of Mathematical Analysis and Applications

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“…In this section we consider Cieśliński's counterexample [1,[6][7][8], the inhomogeneous nonlinear Schrödinger equation…”

Section: An Example the Inhomogeneous Nonlinear Schrödinger Equationmentioning

confidence: 99%

“…The symmetry method [5] and its extension [6][7][8] by Cieśliński take advantage of linearity of the problem. Remarkably enough, certain aspects of this method admit a cohomological interpretation, which will be discussed elsewhere.…”

Section: Extension Procedures Recursion Operatorsmentioning

confidence: 99%

On the Spectral Parameter Problem

Marvan

2009

Acta Appl Math

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“…However, while studing a differential equation, it is not unusual to know only a nonparametric ZCR [4,8,16,19]. Then, in such cases one is naturally faced with the embedding problem of a given nonparametric ZCR α into a nontrivial 1-parameter family α λ of ZCRs.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, due to the importance of this problem, various attempts have been already made to provide any effective embedding method. Among these the symmetry method, first suggested in [8,17] and further developed in the papers [5,4,7], is particularly representative.…”

Section: Introductionmentioning

confidence: 99%