TY - JOUR
T1 - The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions
T2 - I. Direct and inverse scattering theory
AU - Demontis, Francesco
AU - Ortenzi, Giovanni
AU - Sommacal, M.
AU - van der Mee, Cornelis
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
KW - Classical Heisenberg ferromagnet equation
KW - Soliton solutions
KW - Inverse scattering transform
KW - Magnetic droplet
KW - Ferromagnetic materials
U2 - 10.1007/s11587-018-0394-8
DO - 10.1007/s11587-018-0394-8
M3 - Article
VL - 68
SP - 145
EP - 161
JO - Ricerche di Matematica
JF - Ricerche di Matematica
SN - 0035-5038
IS - 1
ER -