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15 February 2025
 
  » arxiv » 1508.0204

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A weak form of the soliton resolution conjecture for high-dimensional fourth-order Schrodinger equations
Tristan Roy ;
Date 2 Aug 2015
AbstractWe prove a weak form of the soliton resolution conjecture of bounded solutions of high-dimensional fourth-order Schrodinger equations. The result relies upon two properties to be proved: the asymptotic frequency localization and the asymptotic spatial localization. In order to prove the asymptotic frequency localization we use the fact that the high frequency pieces of the free solution have better dispersive properties than then lower ones. In order to prove the asymptotic spatial localization, we use the symmetries of the phase of the fundamental solution.
Source arXiv, 1508.0204
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