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 fami lies 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 ot her interesting findings. The latter includes (i) multihumped solitary wave s without even or odd symmetry and (ii) multihumped solitary waves with lar ge separation between their humps which, however, may not be viewed as boun d states of several distinct one-humped solitons.