The Toda system and multiple-end solutions of autonomous planar elliptic problems
Analysis of PDEs
2007-10-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0710.0640,
title = {The Toda system and multiple-end solutions of autonomous planar elliptic problems},
author = {Manuel del Pino and Michał Kowalczyk and Frank Pacard and Juncheng Wei},
journal= {arXiv preprint arXiv:0710.0640},
year = {2007}
}