Annales Henri Poincaré

, Volume 11, Issue 6, pp 1007–1021 | Cite as

On the Renormalization Group Approach to Perturbation Theory for PDEs

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Abstract

We investigate the rigorous application of the renormalization group method to (singular) perturbation theory for nonlinear partial differential equations. As a paradigm, we consider the concrete example of the nonlinear Schrödinger equation with quadratic nonlinearity in three spatial dimensions. We obtain an approximate solution using the RG method together with an estimate of the difference between the true and approximate solutions. Our analysis applies to cases where (space–time) resonances are present.

Keywords

Perturbation Theory Approximate Solution Renormalization Group Inverse Fourier Transform Fractional Integration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of SaskatchewanSaskatoonCanada

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