The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory
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We develop the direct and inverse scattering theory of the linear eigenvalue problem associated with the classical Heisenberg continuous equation with in-plane asymptotic conditions. In particular, analyticity of the scattering eigenfunctions and scattering data, and their asymptotic behaviours are derived. The inverse problem is formulated in terms of Marchenko equations, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided.
KeywordsClassical Heisenberg ferromagnet equation Soliton solutions Inverse scattering transform Magnetic droplet Ferromagnetic materials
Mathematics Subject Classification35C08 35G25 35P25 35Q40 35Q51
The results contained in the present paper have been partially presented in Wascom 2017. The research leading to this article was supported in part by INdAM-GNFM and the London Mathematical Society Scheme 4 (Research in Pairs) grant on “Propagating, localised waves in ferromagnetic nanowires” (Ref No: 41622). We also wish to thank an anonymous referee for his/her valuable comments.
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