Allain, Geneviève; Beaulieu, Anne Solutions on a torus for a semilinear equation. (English) Zbl 1216.35047 Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 2, 371-382 (2011). 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) Keywords:semilinear equation; positive doubly periodic solutions; nonlinear Schrödinger equation; ground-state solution PDFBibTeX XMLCite \textit{G. Allain} and \textit{A. Beaulieu}, Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 2, 371--382 (2011; Zbl 1216.35047) Full Text: DOI