论文标题
NLS方程中的非线性作为恒星图上的阈值现象的来源
Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs
论文作者
论文摘要
我们研究了两个亚临界焦点非线性术语的恒星图上非线性schrödinger方程的基态的存在：标准功率非线性和位于顶点的delta型非线性。我们发现，如果标准的非线性比点宽的非线性强，则仅存在小质量的基态。相反，如果偶然的非线性占上风，则仅存在大量质量的基态。所有接地状态都是径向的，从某种意义上说，它们对每个半线的限制总是相同的功能，并且与孤子尾巴相吻合。最后，如果两个非线性的大小相同，则基态的存在对质量的值不敏感，并且仅在少量半线的图上保持。此外，我们在没有基态的大规模政权中建立了地面状态所属的径向固定状态的轨道稳定性。
We investigate the existence of ground states for the nonlinear Schrödinger Equation on star graphs with two subcritical focusing nonlinear terms: a standard power nonlinearity, and a delta-type nonlinearity located at the vertex. We find that if the standard nonlinearity is stronger than the pointwise one, then ground states exist for small mass only. On the contrary, if the pointwise nonlinearity prevails, then ground states exist for large mass only. All ground states are radial, in the sense that their restriction to each half-line is always the same function, and coincides with a soliton tail. Finally, if the two nonlinearities are of the same size, then the existence of ground states is insensitive to the value of the mass, and holds only on graphs with a small number of half-lines. Furthermore, we establish the orbital stability of the branch of radial stationary states to which the ground states belong, also in the mass regimes in which there is no ground state.
