Suppose you have a scalar field [itex]\psi(x,t)[/itex] subjected to a certain differential equation. Is there an easy way to find at wich (phase) speed dx/dt this field propagates without actually solving the differential equation.(adsbygoogle = window.adsbygoogle || []).push({});

E.g. it is well known the differential equation

[tex]\frac{\partial^2 \psi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \psi}{\partial t^2}[/tex]

has solution with phase speed c

or that

[tex]\frac{\partial^2 \psi}{\partial x^2} = 0 [/tex]

has solutions with an infinite phase speed.

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# Velocity of the solution of a diff. eq.

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