Factorization of the nonlinear Schroedinger equation and applications

2005/09/01 by Swanhild Bernstein, Bernstein, Swanhild · 1 citation
Mathematics · Physics and Astronomy · #30G35 #35F30 #35J10 #35Q55 #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #advanced mathematical theories #math-ph #math.CV #math.MP #msc:30G35 #msc:35F30 #msc:35J10 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.math/0509018

22 pages

arxiv created 2005/09/01 · openalex publication_date 2005/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider factorizations of the stationary and non-stationary Schroedinger equation in Rⁿ which are based on appropriate Dirac operators. These factorizations lead to a Miura transform which is an analogue of the classical one-dimensional Miura transform but also closely related to the Riccati equation. In fact, the Miura transform is a nonlinear Dirac equation. We give an iterative procedure which is based on fix-point principles to solve this nonlinear Dirac equation. The relationship to nonlinear Schroedinger equations like the Gross-Pitaevskii equation are highlighted.

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