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We present a design and protocol to achieve an essential feature of an optical transistor, namely the amplification of input signal with the use of discrete solitons in waveguide arrays. We consider the scattering of a discrete soliton by a reflectionless potential in the presence of a control soliton. We show that at the sharp transition region between full reflectance and full transmittance, the intensity of the reflected or transmitted soliton is highly sensitive to the intensity of the control soliton. This suggests a setup of signal amplifier. For realistic purposes, we modulate the parameters of the reflectionless potential well to achieve a performance of amplifier with a controllable amplification. To facilitate the experimental realization, we calculate the amplification factor in terms of the parameters of the potential well and the input power of the control soliton. The suggested signal amplifier device will be an important component in the all-optical data processing.

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We present a design and protocol to add binary numbers using discrete solitons in waveguide arrays. We show that the nonlinear interaction between discrete solitons in waveguide arrays can be exploited to design half and full adders. By modulating the separation between waveguides and introducing control solitons, we achieve the performance of an XOR gate. We construct the half and full adders using the XOR gate together with the previously-designed OR and AND gates. To facilitate the experimental realization, we calculate the profile of separations between the waveguides that will lead to the performance of the XOR gate.