We present the application of projection operator methods to solving the problem of the propagation and interaction of short optical pulses of different polarizations and directions in a nonlinear dispersive medium. We restrict ourselves by the caseof one-dimensional theory, taking into account material dispersion and Kerr nonlinearity. The construction of operators is delivered in two variants: for the Cauchy problem and for the given boundary regime at the initial point of the propagation half-space x > 0. As a result, we derive a system of four first-order differential equations that describe the interaction of four specified modes. In the construction of projection operators, we use an expansion with respect to a small parameter that characterizes the material dispersion, amplitude, and pulse profile. The results are compared with the vector short pulse equations (VSPE) as well as ours previous, the one for opposite propagated pulses.
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