A weak form of the soliton resolution conjecture for high-dimensional fourth-order Schrodinger equations

2015/08/02 by Tristan Roy, Roy, Tristan
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1508.00204

46 pages. To appear

openalex publication_date 2015/08/02 · arxiv created 2017/03/28 · arxiv updated 2017/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We 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 the lower ones. In order to prove the asymptotic spatial localization, we use the symmetries of the phase of the fundamental solution.

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