The Inverse Scattering Transform for the Elliptic Sinh-Gordon Equation

摘要: The elliptic Sinh-Gordon equation $${{u}_{{xx}}} + {{u}_{{yy}}} = {{\lambda }^{2}}\sinh u$$ (1) appears in plasma physics [1–5] as a two dimensional model describing system of interacting charged particles. Depending on the sign λ2 we can consider both positive and negative temperature states thermal equilibrium [4], corresponding to essentially different solutions eq. (1).