Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.1, pp.67--84

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 1, pp.67-84

Solitons in ferromagnets and the KdV Hierarchy
H. Leblond

The higher order terms in the perturbative expansion that describes KdV solitons propagation in ferromagnetic materials are considered. They satisfy inhomogeneous linearized KdV equations, explicitly written down. The parity and homogeneity properties of the expansion show that half of these equations admit a zero solution. Long time propagation is investigated, through the consideration of the unbounded or secular solutions and a multi-time expansion. It is governed by all equations of the KdV Hierarchy. Major result of the paper is that the multi-scale expansion can be achieved up to any order with all its terms bounded, what is a necessary condition for its convergence.
Key words: KdV Hierarchy, Higher order KdV, KdV solitons, ferromagnets

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