Energy Density (also specific energy) (per unit width and dx)
(due to dispersion relationship)
Maintain only leading order terms ( 
second term -
corresponds to potential energy of the calm water and thus is not considered.
Mean potential energy 
over one period, T:
Mean potential energy over one wave length, L:
So energy over a wave length: (per unit width)
Compare with equation (2-38) of SPM.