Analytical and numerical methods are used to investigate the new localized states of a
surface magnetostatic wave envelope in a ferromagnet–dielectric–metal structure in the
framework of the extended non-linear Schrödinger equation. The problems of the modulation
instability of homogeneous states and long-wavelength modulation of a monochromatic
wave in the vicinity of a ‘zero-dispersion’ point are discussed. The excitation conditions for
a multi-soliton state are analysed. It is shown that a certain threshold amplitude
of the initial distribution should be reached for the excitation of these states,
while no such threshold exists for the one-soliton state. The possibility of the
experimental observation of the above-mentioned non-linear states is discussed.
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