A review of dispersive limits of (non)linear schrödinger-type equations

Ingenuin Gasser*, Chi Kun Lin, Peter A. Markowich

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

75 Citations (Scopus)


In this review paper we present the most important mathematical properties of dispersive limits of (non)linear Schrödinger type equations. Different formulations are used to study these singular limits, e.g., the kinetic formulation of the linear Schrödinger equation based on the Wigner transform is well suited for global-in-time analysis without using WKB-(expansion) techniques, while the modified Madelung transformation reformulating Schrödinger equations in terms of a dispersive perturbation of a quasilinear symmetric hyperbolic system usually only gives local-in-time results due to the hyperbolic nature of the limit equations. Deterministic analogues of turbulence are also discussed. There, turbulent diffusion appears naturally in the zero dispersion limit.

Original languageEnglish
Pages (from-to)501-529
Number of pages29
JournalTaiwanese Journal of Mathematics
Issue number4
Publication statusPublished - Dec 2000
Externally publishedYes


  • Compressible Euler equation
  • Dispersive limit
  • KdV equation
  • Quantum hydrodynamics
  • Wigner transform


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