Cnoidal Wave Solutions to Boussinesq Systems
In this paper, two different techniques will be employed
to study the cnoidal wave solutions of the Boussinesq systems.
existence of periodic traveling wave solutions for a large family of
systems is established by using a topological
Although this result
guarantees the existence of cnoidal wave solutions in a parameter
region in the period and phase speed plane,
it does not provide the uniqueness, nor the non-existence of
such solutions in other parameter regions.
The explicit solutions are then found by
using the Jacobi elliptic function series.
Some of these explicit solutions fall in the parameter region where the cnoidal
wave solutions are proved to exist, and
others do not; so the method with Jacobi elliptic functions provides additional cnoidal wave
solutions. In addition,
the explicit solutions can be used in many ways, such as
in testing numerical code and in testing the stability of
Min Chen (email@example.com)