Molchan Maxim A
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch 7701, South Africa.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056603. doi: 10.1103/PhysRevE.84.056603. Epub 2011 Nov 7.
We study analytically and numerically the linear stability of weakly nonlocal solitons in the parametrically driven nonlinear Schrödinger equation. Two exact solutions are derived in an implicit form. We show analytically that despite the well-known stabilizing properties of nonlocality one of the solitons remains unstable even in the nonlocal case for any values of the dissipation, the damping, and the degree of nonlocality. The second soliton, as compared to its local counterpart, attains wider stable regions in the space of the parameters of the system.
我们通过解析和数值方法研究了参数驱动非线性薛定谔方程中弱非局域孤子的线性稳定性。以隐式形式导出了两个精确解。我们通过解析表明，尽管非局域性具有众所周知的稳定特性，但即使在非局域情况下，对于任何耗散、阻尼和非局域程度的值，其中一个孤子仍然是不稳定的。与局部对应物相比，第二个孤子在系统参数空间中获得了更宽的稳定区域。
