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Existence and uniqueness of the solution to the modified Schrödinger map. (English) Zbl 1082.35140
The author studies the initial value problem for a system of nonlinear Schrödinger equations in two space dimensions (modified Schrödinger map) which is derived from Schrödinger maps from × 2 to the unit sphere S 2 or to the hyperbolic space 2 by using appropriate gauge change. The existence and uniqueness of the solution was known for data in H s ( 2 ) with s>1. In this paper the local existence of the solution is proved for the initial data in H s ( 2 ) with s>1/2. The uniqueness of the solution is also proved when the data belong to H 1 ( 2 ).
MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35G25Initial value problems for nonlinear higher-order PDE