The Toda system and multiple-end solutions of autonomous planar elliptic problems

Details The Toda system and multiple-end solutions of autonomous planar elliptic problems The Toda system and multiple-end solutions of autonomous planar elliptic problems

2007-10-02

arxiv.org/abs/0710.0640v1

Mathematics

Analysis of PDEs

Scientific paper

We construct a new class of positive solutions for a classical semilinear elliptic problem in the plane which arise for instance as the standing-wave problem for the standard nonlinear Schr\"odinger equation or in nonlinear models in Turing's theory biological theory of pattern formation such as the Gray-Scott or Gierer-Meinhardt systems. The solutions we construct have the property that their energy over a ball of radius R grows linearly with R as R tends to infinity. These solutions are strongly related to the solutions of a Toda system.

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