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The Matrix Nonlinear Schrödinger Equation in Dimension 2

✍ Scribed by Liu Zuhan; Michael Pedersen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
92 KB
Volume
262
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we study the existence of global solutions to the Cauchy problem Ž . 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 ëquation for which existence of solutions has been studied by many authors.

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