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Zbl 0627.35039
Ting, A.C.; Chen, H.H.; Lee, Y.C.
Exact solutions of a nonlinear boundary value problem: The vortices of the two-dimensional sinh-Poisson equation.
(English)
[J] Physica D 26, 37-66 (1987). ISSN 0167-2789

The 2-dimensional sinh-Poisson equation $\Delta u+\lambda\sp 2 \sinh (u)=0$ 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.
[E.Malec]
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
35R30 Inverse problems for PDE
35B32 Bifurcation (PDE)
76X05 Plasmic flows

Keywords: sinh-Poisson equation; inverse scattering method; Lax pair; bifurcate

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