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Zbl 1082.35140
Kato, Jun
Existence and uniqueness of the solution to the modified Schrödinger map. (English)
[J] Math. Res. Lett. 12, No. 2-3, 171-186 (2005). ISSN 1073-2780

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 $\bbfR\times \bbfR^2$ to the unit sphere $S^2$ or to the hyperbolic space $\bbfH^2$ by using appropriate gauge change. The existence and uniqueness of the solution was known for data in $H^s(\bbfR^2)$ with $s> 1$. In this paper the local existence of the solution is proved for the initial data in $H^s(\bbfR^2)$ with $s> 1/2$. The uniqueness of the solution is also proved when the data belong to $H^1(\bbfR^2)$.
[Viorel Iftimie (Bucureşti)]

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35G25 Initial value problems for nonlinear higher-order PDE

Keywords: nonlinear Schrödinger equations; modified Schrödinger map; initial value problem

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Zentralblatt MATH Berlin [Germany]