Solutions on a torus for a semilinear equation

@article{Allain2011SolutionsOA,
  title={Solutions on a torus for a semilinear equation},
  author={Genevi{\`e}ve Allain and Anne Beaulieu},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  year={2011},
  volume={141},
  pages={371 - 382}
}
  • G. Allain, Anne Beaulieu
  • Published 1 April 2011
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
We are interested in the positive doubly periodic solutions, which are even in each variable, of a stationary nonlinear Schrödinger equation in ℝ2, 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. 

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