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We study the mobility of solitons in second-harmonic-generating lattices.Contrary to what is known for their cubic counterparts, discrete quadraticsolitons are mobile not only in the one-dimensional (1D) setting, but also intwo dimensions (2D). We identify parametric regions where an initial kickapplied to a soliton leads to three possible outcomes, namely, staying put,persistent motion, or destruction. For the 2D lattice, it is found that, forthe solitary waves, the direction along which they can sustain the largest kickand can attain the largest speed is the diagonal. Basic dynamical properties ofthe discrete solitons are also discussed in the context of an analyticalapproximation, in terms of an effective Peierls-Nabarro potential in thelattice setting.Comment: 4 page

Mobility of Discrete Solitons in Quadratically Nonlinear Media