Bobenko, A. I. Eigenfunctions of the Dirichlet and Neumann boundary value problems on a rectangle for the elliptic sine-Gordon equation. (Russian. English summary) Zbl 0706.35111 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 179, 32-36 (1989). The eigenfunctions of the elliptic sinh-Gordon equation in a rectangle subject to Dirichlet and Neumann boundary conditions are discussed. All solutions of the boundary value problems are found explicitly via finite gap integration. Possible applications in differential geometry are indicated. Reviewer: N.Vulchanov Cited in 1 ReviewCited in 3 Documents MSC: 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35J60 Nonlinear elliptic equations 35Q53 KdV equations (Korteweg-de Vries equations) 53A99 Classical differential geometry Keywords:eigenfunctions; elliptic sinh-Gordon equation; Dirichlet and Neumann boundary conditions PDFBibTeX XMLCite \textit{A. I. Bobenko}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 179, 32--36 (1989; Zbl 0706.35111) Full Text: EuDML