双稳态非简并链中跃迁前沿的传播：模型依赖性和普适性
Propagation of transition front in bi-stable nondegenerate chains: model dependence and universality
摘要：
本文研究了具有双稳态非简并在位势的一维链中跃迁前沿的传播。如果采用链中的线性耦合和分段线性的现场力，那么就有可能得到已知的前和伴随的振荡尾的精确解。我们证明，这些解决方案基本上是非鲁棒的。具有相同基本参数（势垒的高度和坐标、能量效应和势阱之间的距离）的现场势的各种近似导致实质上不同的波前速度。此外，包含甚至弱的最近邻非线性大幅修改前端的结构和参数。前区的能量集中导致非线性项占主导地位。事实证明，动态可以有效地研究在一个等效的模型与一个单一的自由度。这种估计导致准确的预测的前端速度和参数的振荡尾巴。此外，它证明了解决方案是强大的-精确形状的现场潜在的微弱影响的前端参数。这一发现也符合简化模型，因为后者只调用一般的形状特征的现场电位。
英文摘要：
We consider a propagation of transition fronts in one-dimensional chains with bi-stable nondegenerate on-site potential. If one adopts linear coupling in the chain and piecewise linear on-site force, then it is possible to develop well-known exact solutions for the front and accompanying oscillatory tail. We demonstrate that these solutions are essentially non-robust. Various approximations for the on-site potential with the same basic parameters (height and coordinate of the potential barrier, energy effect and distance between the potential wells) lead to substantially different front velocities. Besides, inclusion of even weak nearest neighbor nonlinearity drastically modifies the front structure and parameters. The energy concentration in the front zone leads to a dominance of the nonlinear term. It turns out that the dynamics can be efficiently studied in terms of an equivalent model with a single degree of freedom. This estimation leads to accurate prediction of the front velocity and parameters of the oscillatory tail. Moreover, it turns out that the solution is robust - exact shape of the on-site potential weakly effects the front parameters. This finding also conforms to the simplified model, since the latter invokes only the general shape characteristics of the on-site potential.
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