The parametrically driven, damped NLS equation is shown to describe the dynamics of small-amplitude breathers of the easy-plane ferromagnet and the long Josephson junction under the influence of the parametric pumping and dissipation. The soliton solutions are found exactly and stability problem for the dissipative case is reduced rigorously to the one for the undamped soliton.
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Barashenkov et al. (1991) studied this question.
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