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Exact solutions of a nonlinear boundary value problem: The vortices of the two-dimensional sinh-Poisson equation. (English) Zbl 0627.35039
The 2-dimensional sinh-Poisson equation Δu+λ 2 sinh(u)=0 with a zero boundary condition on a square is solved via the inverse scattering method. The Lax pair of the system is similar to that of the sine-Gordon equation. The solutions appear to bifurcate from u=0 at eigenvalues of the associated linear problem.
Reviewer: E.Malec
35J65Nonlinear boundary value problems for linear elliptic equations
35R30Inverse problems for PDE
35B32Bifurcation (PDE)
76X05Ionized gas flow in electromagnetic fields; plasmic flow