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Solutions on a torus for a semilinear equation. (English) Zbl 1216.35047

Summary: We are interested in the positive doubly periodic solutions, which are even in each variable, of a stationary nonlinear Schrödinger equation in \(\mathbb R^2\), with a small parameter. For any pair of periods \((2a,2b)\), we construct a branch of solutions that concentrate uniformly to the ground-state solution of the equation.

MSC:

35J61 Semilinear elliptic equations
35B09 Positive solutions to PDEs
35B10 Periodic solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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