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I suppose it is related to hyperbolic partial differential equations.

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Example of a hyperbolic system, the first order wave equation: $ {\partial \underline{U} \over \partial t} + \underline{A} {\partial \underline{U} \over \partial x} = 0$

The term hyperbolic means that:

  • The eigenvalues of the $m \times m$ Jacobian matrix ($\underline A $) are all real
  • There is a corresponding set of $m$ linearly independent eigenvectors

This allows decomposition of the system into a linear combination of these eigenvectors, where the corresponding eigenvalues of $\underline{A}$ give the wave speeds.

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