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We propose an exactly solvable model of soliton-based pulse control that describes the physically important situation when the soliton period is much longer than the length of the coupling region in a nonlinear fiber coupler. This case can occur, e.g., in fused-fiber couplers. We demonstrate that the problem of soliton interaction and switching in such a coupler can be reduced to a linear relation between the fields before and after interaction. The soliton states can be found by solution of two Zakharov–Shabat eigenvalue problems associated with a pair of decoupled nonlinear Schrödinger equations. Various regimes of soliton control, switching, and splitting in this model are discussed. In particular, we show that perfect pulse switching from one arm of the coupler to the other resembles the switching of continuous waves in linear couplers, whereas the phase-controlled switching of solitons is similar to that in nonlinear directional couplers. We also describe other schemes of soliton control, including pulse compression through fusion of two fundamental solitons.