EXISTENCE OF TRAVELING-WAVE SOLUTIONS
TO BOUSSINESQ SYSTEMS
In this manuscript, the existence of traveling-wave solutions
to Boussinesq systems
\eta_t + u_x + (\eta u)_x + a u_{xxx}-b \eta_{xxt} = 0,
u_t +\eta_x + uu_x + c\eta_{xxx}- d u_{xxt} = 0,
is established. We prove that all the systems with a<0, c<0 and b=d
exhibit traveling-wave solutions with small propagation speeds.
The result complements our earlier work [6] on a restricted family of the
systems where both existence and stability of traveling-wave solutions
were established in the presence of large surface tension, namely when
a + b + c + d<0.
Min Chen (chen@math.purdue.edu)