Does the complex deformation of the Riemann equation exhibit shocks?

Carl M. Bender, Joshua Feinberg

Research output: Contribution to journalArticlepeer-review


The Riemann equation ut + uux = 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, ut - iu(iux)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. When ε is an odd integer, the shock-formation time is calculated explicitly.

Original languageEnglish
Article number244004
JournalJournal of Physics A: Mathematical and Theoretical
Issue number24
StatePublished - 20 Jun 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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