黎曼方程的复杂变形是否表现出激波？
Does the complex deformation of the Riemann equation exhibit shocks?
摘要：
黎曼方程$u_t+uu_x=0$描述了一维无加速度理想流体，其解通常在有限时间内产生激波。该方程是$\cP\cT$对称的。利用特征带方法精确求解了该方程的一个单参数$\cP\cT$不变的复变形$u_t-iu(iu_x)^ε= 0$（$ε$ real），并证明了在实初始条件下，除非$ε$是奇数，否则激波不会发展.
英文摘要：
The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is $\cP\cT$ symmetric. A one-parameter $\cP\cT$-invariant complex deformation of this equation, $u_t-iu(iu_x)^ε= 0$ ($ε$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $ε$ is an odd integer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
