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Wave Equations and Energy Density

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For a solution of the wave equation with p=T=C=1 the energy density is defined as e=1/2 (U_t ^2 + U_x ^2) and the momentum density as p=U_t*U_x

Show that de/dt=dp/dx and dp/dt=de/dx

Show that both e(x,t) and p(x,t) also satisfy the wave equation

http://tosio.math.toronto.edu/pdewiki/index.php/2006APM346Midterm1

It's problem number 4 from this site.

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