N-soliton solutions for second-harmonic generation with account of the Kerr effect

For second-harmonic generation the optical Kerr effect causes a cross-phase modulation between ground and harmonic waves as well as self-phase modulat ions of both waves. When only cross-phase modulation is taken into account this system proves to be integrable by the inverse scattering method. Here Darboux/Backlund transformations are established, and the resulting phenome nology of soliton solutions is discussed and depicted.