In this report, we study theoretically and numerically the soliton propagation of laser radiation in the medium with quadratic and cubic nonlinear response. We show that, for high-intensity femtosecond pulses with a large phase mismatch of the interacting waves, soliton propagation of two-color laser radiation with similar peak intensities of interacting waves is possible. Our investigation is based on two coupled nonlinear Schrödinger equations. Using a multiscale approach, we derive an approximate analytical solution for two-color laser radiation propagation in the soliton mode. Based on numerical simulation, high-efficient frequency down conversion is demonstrated when switching the two-color soliton mode to the soliton mode with high peak intensity at the fundamental frequency.
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