Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.
This paper considers a non-linear wave equation arising in fluid mechanics.
The exact traveling wave solutions of this equation are given by using
G'/G-expansion method. This process can be reduced to solve a system of
determining equations, which is large and difficult. To reduce this process,
we used Wu elimination method. Example shows that this method is effective.
By using the tanh-coth method, we obtained some travelling wave solutions of two well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation and the higher-order improved Boussinesq equation. We show that the tanh-coth method is a useful, reliable, and concise method to solve these types of equations.
Travelling wave solutions for higher-order wave equations of KDV type (III)