  The two-field equations governing fully nonlinear dynamics of the drift wave
(DW) and geodesic acoustic mode (GAM) in the toroidal geometry are derived in
nonlinear gyrokinetic framework. Two stages with distinctive features are
identified and analyzed. In the linear growth stage, the set of nonlinear
equations can be reduced to the intensively studied parametric decay
instability (PDI), accounting for the spontaneous resonant excitation of GAM by
DW. The main results of previous works on spontaneous GAM excitation, e.g., the
much enhanced GAM group velocity and the nonlinear growth rate of GAM, are
reproduced from numerical solution of the two-field equations. In the fully
nonlinear stage, soliton structures are observed to form due to the balancing
of the self-trapping effect by the spontaneously excited GAM and kinetic
dispersiveness of DW. The soliton structures enhance turbulence spreading from
DW linearly unstable to stable region, exhibiting convective propagation
instead of typical linear dispersive process, and is thus, expected to induce
core-edge interaction and nonlocal transport.
