Multicomponent generalization of the hierarchy of the Landau-Lifshitz equation

Golubchik, I. Z.; Соколов, В. В.

doi:10.1007/bf02551067

Cited by 46 publications

(75 citation statements)

References 6 publications

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“…We would like to thank V.V.Sokolov for drawing our attention to paper [3]. This work has been supported in part by the Royal Society and the Bulgarian academy of sciences (joint research project "Reductions of Nonlinear Evolution Equations and analytic spectral theory").…”

Section: Acknowledgementsmentioning

confidence: 99%

Reductions of integrable equations onA.III-type symmetric spaces

Gerdjikov¹,

Михайлов²,

Valchev³

2010

J. Phys. A: Math. Theor.

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Abstract. We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU (N )/S(U (N − k) × U (k)). We use the Cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic Lax operators to this symmetric space. The symmetries of the Lax operator are inherited by the fundamental analytic solutions and give a characterization of the corresponding Riemann-Hilbert data.

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Section: Acknowledgementsmentioning

confidence: 99%

Reductions of integrable equations onA.III-type symmetric spaces

Gerdjikov¹,

Михайлов²,

Valchev³

2010

J. Phys. A: Math. Theor.

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“…We note that for n > 4, the hierarchy of vector equation (26) contains no nontrivial analogue of the Landau-Lifshitz equation. This was noted in [29] and proved rigorously in [16].…”

Section: Integrable Hierarchies Associated With the Algebrag +mentioning

confidence: 69%

“…In the case n > 4, Eq. (26) was first obtained in [29] using the technique for dressing Lie algebras of formal power series; it was also obtained in [16] using another method. We note that for n > 4, the hierarchy of vector equation (26) contains no nontrivial analogue of the Landau-Lifshitz equation.…”

Section: Integrable Hierarchies Associated With the Algebrag +mentioning

confidence: 99%

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Quasigraded lie algebras, Kostant-Adler scheme, and integrable hierarchies

Skrypnyk

2005

Theor Math Phys

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Using special "anisotropic" quasigraded Lie algebras, we obtain a number of new hierarchies of integrable nonlinear equations in partial derivatives admitting zero-curvature representations. Among them are an anisotropic deformation of the Heisenberg magnet hierarchy, a matrix and vector generalization of the Landau-Lifshitz hierarchies, new types of matrix and vector anisotropic chiral-field hierarchies, and other types of "anisotropic" hierarchies.

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“…A vector generalization of a higher symmetry of the Landau-Lifshitz equation [2] also provides a known example,…”

Section: Introductionmentioning

confidence: 99%