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.

It is known that variational methods are the most powerful tool for studying the Coulomb three-body bound-state problem. However, they often suffer from loss of stability when the number of basis functions increases. This problem can be cured by applying the multiprecision package designed by D. H. Bailey. We consider variational basis functions of the type exp(Ϫ␣ n r 1 Ϫ␤ n r 2 Ϫ␥ n r 12) with complex exponents. The method yields the best available energies for the ground states of the helium atom and the positive hydrogen molecular ion as well as many other known atomic and molecular systems.

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