Singular limits of the Klein-Gordon equation

Chi Kun Lin, Kung-Chien Wu

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We establish the singular limits, including semiclassical, nonrelativistic and nonrelativistic-semiclassical limits, of the Cauchy problem for the modulated defocusing nonlinear Klein-Gordon equation. For the semiclassical limit, H 0, we show that the limit wave function of the modulated defocusing cubic nonlinear Klein-Gordon equation solves the relativistic wave map and the associated phase function satisfies a linear relativistic wave equation. The nonrelativistic limit, c ∞, of the modulated defocusing nonlinear Klein-Gordon equation is the defocusing nonlinear Schrödinger equation. The nonrelativistic-semiclassical limit, H 0, c = H ∞ for some α > 0, of the modulated defocusing cubic nonlinear Klein-Gordon equation is the classical wave map for the limit wave function and a typical linear wave equation for the associated phase function.

Original languageEnglish
Pages (from-to)689-711
Number of pages23
JournalArchive for Rational Mechanics and Analysis
Volume197
Issue number2
DOIs
Publication statusPublished - 2010 Apr 21

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Singular limits of the Klein-Gordon equation'. Together they form a unique fingerprint.

Cite this