Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics

Possibility of integrating by the inverse scattering problem method is investigated for equations describing interaction of colliding quasimonochromatic wave packets in a medium with cubic nonlinearity. It is shown that all the integrable cases are restricted to the already known integrable case of the equations of “unsymmetrical chiral field” which corresponds to propagation of waves without the Kerr self-interaction.