Yang Jianke, Pelinovsky Dmitry E
Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jan;67(1 Pt 2):016608. doi: 10.1103/PhysRevE.67.016608. Epub 2003 Jan 24.
We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point, where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly stable in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.
我们通过解析和数值方法研究了（2 + 1）维饱和非线性介质中涡旋和偶极矢量孤子的存在性、唯一性和稳定性。我们在分岔点附近构造了涡旋和偶极矢量孤子的微扰级数展开式，此时涡旋和偶极分量较小。我们表明这两种解都从同一个分岔点唯一地分岔出来。我们还证明了涡旋和偶极矢量孤子在分岔点附近都是线性稳定的。远离分岔点时，涡旋孤子族通过振荡不稳定性变得线性不稳定，而偶极孤子族在整个存在域内保持稳定。此外，我们表明一个不稳定的涡旋孤子要么分裂成一个旋转的偶极孤子，要么分裂成两个旋转的基本孤子。
