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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The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its "excited" states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher order spatial or mixed derivatives. The dispersive sine-Gordon, double and triple sine-Gordon, and piecewiselinear models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.PACS number(s): 03.40.Kf, 47.20.Ky, 47.35.+i, 62.30.+d.

Chaotic regimes of the microwave energy absorption are experimentally observed and analyzed for two-dimensional metallorganic antiferromagnet (NH 3 ) 2 (CH 2 ) 4 MnCl 4 at low temperatures under the conditions of nonlinear antiferromagnetic resonance. Relaxation oscillations of energy absorption are investigated in detail. Their frequency spectra, frequency-amplitude characteristics, and dependences of absorbed power on driving power and static magnetic field are studied. It is shown that the dynamics of relaxation oscillations undergoes a transition to chaos by "irregular periods". Peculiarities of the transition are described consistently. Among other things, the conditions for the emergence of energy absorption regimes with a spike-like and a saw-tooth signal structure are determined, and the characteristics of chaotic oscillations such as the dimensions of strange attractors are calculated. The chaotic dynamics is found to be high-dimensional with a large contribution from noise which is of deterministic origin in the antiferromagnet under in-1 vestigation.