  We present a model of soliton propagation in waveguides with quadratic
nonlinearity. Criteria for solitons to exist in such waveguides are developed
and two example nano-waveguide structures are simulated as proof of concept.
Interactions between quadratic solitons and dispersive waves are analysed
giving predictions closely matching soliton propagation simulations. The
example structures are found to support five different regimes of soliton and
quasi-soliton existence. Pulse propagation in these example waveguides has been
simulated confirming the possibility of soliton generation at experimentally
accessible powers. Simulations of multi-soliton generation, Cherenkov radiation
and quasi-solitons with opposite signs of dispersion in the fundamental and
second harmonic are also presented here.
