期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 41, 期 24, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/41/24/244004
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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 PT symmetric. A one-parameter PT-invariant complex deformation of this equation, u(t) - iu(iu(x))(epsilon) = 0 (epsilon real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless epsilon is an odd integer. When epsilon is an odd integer, the shock-formation time is calculated explicitly.
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