The nonlinear Schrödinger equation, with complex coefficients that describe growth and damping, is considered. An exact stationary soliton solution is found for arbitrary growth and damping strength.
This review summarizes recent experimental data on imploding z-pinches and their radiation output, and gives an overview of theoretical issues concerning radiation production in the pinch plasma. A z-pinch plasma is created when the current from a fast, powerful electrical generator compresses and heats a small amount of material between the electrodes. The hot, dense plasma emits copious amounts of radiation extending from the visible to the x-ray region. With a 10-TW electrical discharge the radiative power may be a few TW, with an energy per pulse of up to tens of kilojoules. Our interest is mainly in the photons with energy around 1 keV, which are useful in x-ray lithography, microscopy, surface studies, and other applications.
The Benjamin–Ono equation that describes nonlinear internal waves in a stratified fluid is solved by a pole expansion method. The dynamics of poles which characterize solitons is shown to be identical to the well-known integrable N-body problem of Calogero, Moser, and Sutherland.
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