  We analytically and numerically study the direct soliton generation in a
cw-pumped doubly resonant degenerate optical parametric oscillator via pump
frequency scanning. By means of bifurcation and linear stability analysis of
the homogeneous solutions, we discriminate distinctive soliton forming
mechanisms and corresponding dynamics, depending on pump and signal group
velocity dispersions (GVDs). To the best of our knowledge, this is the first
study regarding the dynamics of pure quadratic solitons. In addition, we
discuss how to extend soliton existing regime and easily access quadratic
soliton by introducing modulation instabilities through the adjustment of pump
and signal GVDs. Our study will benefit the theoretical cavity design and
experimental realization for pure quadratic solitons.
