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Just wondering:

  1. How to solve ultrahyperbolic PDEs? Is there any analytical solution for linear ultrahyperbolic PDEs?
  2. If there are only numerical solutions, are the solutions' behavior similar to those of nonlinear eqns? I mean, like an anharmonic oscillator, chaotic but deterministic?

Information of reference books is also welcomed - but better not too specialized in math. I am an engineering student with very very limited math skills.

Thanks :)

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    I provided an answer below in the context of the initial value problem (since you mentioned the word "deterministic" [which by the way, is not true of the ultrahyperbolic equations]). If you mean something else, please edit the question to clarify. Note also that the ultrahyperbolic equation is closely related to the Radon and X-ray transforms. So there are also lots of highly theoretical literature about it, usually under the guise of symmetric spaces and harmonic analysis on them.2010-12-17

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