We consider the equation
$\Delta u+{{u}_{yy}}+f(x,u) = 0,\quad (x,y)\in {{\mathbb{R}}^{N}}\times \mathbb{R}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( 1 \right)$
where $ f $ is sufficiently regular, radially symmetric in $ x $, and $ f(\cdot,0)\equiv 0 $. We give sufficient conditions for the existence of solutions of (1) which are quasiperiodic in $ y $ and decaying as $ |x|\to\infty $ uniformly in $ y $. Such solutions are found using a center manifold reduction and results from the KAM theory. A required nondegeneracy condition is stated in terms of $ f_u(x,0) $ and $ f_{uu}(x,0) $, and is independent of higher-order terms in the Taylor expansion of $ f(x,\cdot) $. In particular, our results apply to some quadratic nonlinearities.
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