In this paper, new exact traveling wave solutions for the coupling Boiti-
Leon-Pempinelli system are obtained by using two important different methods. The first is
the modified extended tanh function methods which depend on the balance rule and the
second is the Ricatti-Bernoulli Sub-ODE method which doesn’t depend on the balance rule.
The solitary waves solutions can be derived from the exact wave solutions by give the
parameters a special value. The consistent and inconsistent of the obtained solutions are
studied not only between these two methods but also with that relisted by the other methods.