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 language | English |
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Journal | Journal of Mathematical Analysis and Applications |
Volume | 262 |
Issue number | 1 |
Pages (from-to) | 388-399 |
ISSN | 0022-247X |
DOIs | |
Publication status | Published - 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