Solitons near avoided mode crossings in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>?</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> nanowaveguides

We present a model for ${\ensuremath{\chi}}^{(2)}$ waveguides accounting three modes, two of which make an avoided crossing at the second harmonic wavelength. introduce linearly coupled pure modes and adjust coupling to replicate waveguide dispersion near crossing. Analysis nonlinear system reveals continuous wave (CW) solutions across much parameter space prevalence its modulational instability. also predict existence avoided-crossing solitons, study peculiarities their dynamics spectral properties, include formation pedestal in pulse tails associated pronounced peaks. Mapping these solitons onto linear diagrams, we connections between CW stability. simulate two-color soliton generation from single-frequency pump back up stability properties.