PT对称变形shock waves
PT-symmetrically deformed shock waves
摘要：
我们调查了一大类非线性波方程，它允许冲击波的形成，这些解决方案的行为时，他们是PT对称变形。对于实数解，我们发现它们被转化为一阶导数不连续的峰值解。我们调查的系统包括PT对称变形的无粘Burgers方程最近研究的本德和Feinberg，我们表明，它不发展任何冲击，而是峰。在这种情况下，我们利用罕见的事实，PT-变形可以提供一个明确的地图发现Curcillary和Fairlie一起的属性，即未变形的方程可以解决的方法的特征。我们概括的地图，并观察到这种类型的行为的所有整数值的变形参数ε。这些峰值是通过PT变形将多值自回避激波轮廓映射为多值自交叉函数而形成的。对于一些变形参数，我们还研究了变形的复杂的解决方案，并证明，在这种情况下，变形机制导致的不连续性。
英文摘要：
We investigate for a large class of nonlinear wave equations, which allow for shock wave formations, how these solutions behave when they are PT-symmetrically deformed. For real solutions we find that they are transformed into peaked solutions with a discontinuity in the first derivative instead. The systems we investigate include the PT-symmetrically deformed inviscid Burgers equation recently studied by Bender and Feinberg, for which we show that it does not develop any shocks, but peaks instead. In this case we exploit the rare fact that the PT-deformation can be provided by an explicit map found by Curtright and Fairlie together with the property that the undeformed equation can be solved by the method of characteristics. We generalise the map and observe this type of behaviour for all integer values of the deformation parameter epsilon. The peaks are formed as a result of mapping the multi-valued self-avoiding shock profile to a multi-valued self-crossing function by means of the PT-deformation. For some deformation parameters we also investigate the deformation of complex solutions and demonstrate that in this case the deformation mechanism leads to discontinuties.
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