具有PT-对称非线性的连续和离散薛定谔系统
Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
摘要：
我们研究了具有宇称-时间（PT）不变非线性的连续和离散薛定谔系统的动力学行为。我们表明，这样的方程的行为在一个根本不同的方式比他们的非线性薛定谔同行。特别地，PT对称非线性薛定谔方程可以同时支持亮孤子解和暗孤子解。此外，我们还研究了这个PT非线性薛定谔方程的二元离散形式。通过获得基本的不变量，我们表明，该系统是完全可积的，我们确定的PT对称性破缺条件。这种安排是独特的，因为例外点完全由非线性本身决定。
英文摘要：
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a two-element discretized version of this PT nonlinear Schrödinger equation. By obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself.
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