Examples
By a linear change of variables, any equation of the form
with
can be transformed to the wave equation, apart from lower order terms which are inessential for the qualitative understanding of the equation. This definition is analogous to the definition of a planar hyperbola.
The one-dimensional wave equation:
is an example of a hyperbolic equation. The two-dimensional and three-dimensional wave equations also fall into the category of hyperbolic PDE.
This type of second-order hyperbolic partial differential equation may be transformed to a hyperbolic system of first-order differential equations.
Read more about this topic: Hyperbolic Partial Differential Equation
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