[en] High statistics data for the reactions K^+-p → K^+-π⁺n at 13 GeV were obtained in a spectrometer experiment performed at SLAC. For each reaction, a t-dependent parametrization of the production amplitudes provides information on both the Kπ mass dependence of the production mechanisms and on Kπ scattering. Knowledge of the t-dependence then allows a calculation of the Kπ partial wave amplitudes for Kπ masses from 0.7 to 1.9 GeV. Besides the leading J/sup P/ = 1^-, 2⁺, and 3^- resonances at M/sub Kπ/ = 0.896, 1.433, and 1.78 GeV, there is evidence in two of the four possible partial wave solutions for a broad P-wave resonant-like structure in the region of 1700 MeV. the K⁺π⁺ reaction is dominated by S-wave scattering with a total cross section of 5.2 mb. The I = ¹/₂ S-wave magnitude rises slowly and smoothly to a maximum near 1400 MeV, but then decreases rapidly between 1400 and 1600 MeV. This structure may possibly be associated with an S-wave resonance near 1500 MeV. Both the I = ¹/₂ S-wave below 1400 MeV and the I = ³/₂ S-wave are well described by an effective range parametrization