Quadratic solitary waves in a counterpropagating quasi-phase-matched configuration.

We demonstrate the possibility of self-trapping of optical beams by use of quasi phase matching in a counterpropagating configuration in quadratic media. We also show the predominant stability of these beams and estimate the power level required for their observation.

Nonlinear dynamics of higher-order solitons near the oscillatory instability threshold.

Nonlinear theory describing the dynamics of solitons in the vicinity of oscillatory instability threshold with a low frequency offset is developed. The theory is tested on the example of parametric degenerate four-wave mixing. All major predictions of our theory are in agreement with the results of direct numerical modeling.

Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing.

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of nonfundamental (multihumped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two types of soliton bifurcations and other interesting findings. The latter includes (i) multihumped solitary waves without even or odd symmetry and (ii) multihumped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.