Statistical equilibrium states of a two-dimensional guiding-center plasma are described by the solutions of a nonlinear elliptic partial differential equation, the sinh-Poisson equation ∇²Φ+λ²sinhΦ=0, with conducting rectangular boundary. We present here the first general analytic solutions to such a nonlinear boundary-value problem. Some of these solutions were obtained previously only through numerical means. Explicit construction of the solutions shows nonlinear superposition among the solutions.
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Ting et al. (1984) studied this question.
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