论文标题
新型的非线性schrödinger方程的精确分析解：晶格上的孤立量子波
Exact analytical solution of a novel modified nonlinear Schrödinger equation: solitary quantum waves on a lattice
论文作者
论文摘要
提出了一种新颖的修改非线性schrödinger方程。通过行驶波Ansatz，方程将转换为非线性颂歌，然后通过该方程进行精确和分析的求解。用波形和波速度表征孤子解，这些特性对方程中参数的依赖性详细介绍。发现某些参数设置产生了独特的波形，而另一些参数设置产生了堕落，每组参数值有两个不同的波形。确定了参数空间的Uni-Waveform和Bi-Waveform区域。还发现每个波形都有两种传播模式，具有共同的方向性，但速度不同。最后，该方程被证明是通过共同振荡的平面晶格与激子相互作用的量子机械激子（例如电子）传播的模型。讨论了孤子解决方案的物理含义。
A novel modified nonlinear Schrödinger equation is presented. Through a travelling wave ansatz, the equation is transformed into a nonlinear ODE which is then solved exactly and analytically. The soliton solution is characterised in terms of waveform and wave speed, and the dependence of these properties upon parameters in the equation is detailed. It is discovered that some parameter settings yield unique waveforms while others yield degeneracy, with two distinct waveforms per set of parameter values. The uni-waveform and bi-waveform regions of parameter space are identified. It is also found that each waveform has two modes of propagation with shared directionality but distinct speeds. Finally, the equation is shown to be a model for the propagation of a quantum mechanical exciton, such as an electron, through a collectively-oscillating plane lattice with which the exciton interacts. The physical implications of the soliton solution are discussed.
