The matrix nonlinear Schrodinger equation in dimension 2

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Abstract

In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence is obtained for this equation. This condition is in terms of an exact stationary solution of a semilinear elliptic equation. In the scalar case, the MNLS reduces to the well-known cubic nonlinear Schrodinger equation for which existence of solutions has been studied by many authors. (C) 2001 Academic Press.
Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
Volume262
Issue number1
Pages (from-to)388-399
ISSN0022-247X
DOIs
Publication statusPublished - 2001

Keywords

  • Matrix nonlinear Schrodinger equation
  • Cauchy problem
  • Ground state solution
  • Waves and wave propagation: general mathematical aspects
  • Algebra, set theory, and graph theory
  • Initial value problems
  • Matrix algebra
  • Nonlinear differential equations
  • Schrodinger equation
  • Global solutions
  • Global existence
  • Semilinear elliptic equation
  • Cubic nonlinear Schrodinger equation
  • Matrix nonlinear Schrödinger equation

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