Double hump solitary waves in quadratic media with walk-off - domain of existence, stability and decay scenarios

We analytically determine the domain of existence of double hump solitary w ave solutions in quadratic media with walk-off. Although a linear stability analysis reveals that these solutions are always unstable the instability gain can be very small for certain parameters. This has important implicati ons for all-optical switching applications. The ultimate decay is prompted by the destruction of an exact phase difference pi between the two humps of the fundamental frequency wave and follows different scenarios.