  Boussinesq equation belongs to Korteweg-de Vries kind of equations (Han &
Yarkony, 2011). Equation describes the motion of long waves in two dimensions
under the gravitation (Han & Yarkony, 2011). Here, we differentiate u = u(x, t)
to the needed order. With c=-1 we have well-posed Boussinesq equation, while
with c=1 not well-posed classical Boussinesq equation (Gradinaru, Hagedorn, &
Joye, 2010). In physical research of nonlinear waves spread in waveguides, it
is necessary to take into account the interaction of waveguides with external
environment (Berezhkoyskii, 2011). Therefore, the possibility of energy
exchange through the outer surface of waveguides, is also should be taken into
account (Berezhkoyskii, 2011). When the energy exchange between a rod and
external environment occurs, it is important to estimate the deformation
dispersion of wave in viscous environment (Han & Yarkony, 2011).
