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Babich, M. V.; Bordag, L. A.

Qualitative investigation of the three-phase solutions of the sine-Laplace equation. (English. Russian original) Zbl 0930.35060

J. Math. Sci., New York 94, No. 4, 1568-1580 (1999); translation from Zap. Nauchn. Semin. POMI 235, 199-216 (1996).
Summary: Real three-phase solutions of the sine-Laplace equation are constructed. All smooth and singular real doubly periodic solutions are found. The corresponding three-dimensional theta functions are reduced to the elliptic Jacobi functions. Some classes of solutions with symmetries giving possibilities for physical applications are determined.

Cited in 1 Document

MSC:

35J60 Nonlinear elliptic equations
35B10 Periodic solutions to PDEs
82D50 Statistical mechanics of superfluids
82D55 Statistical mechanics of superconductors

Keywords:

singular real doubly periodic solutions; theta functions; elliptic Jacobi functions

Citations:

Zbl 0924.00015
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Full Text: DOI EuDML

References:

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