The variable separated ODE method for travelling wave solutions for the Boussinesq-double sine-Gordon and the Boussinesq-double sinh-Gordon equations

Travelling wave solutions for the Boussinesq-double sine-Gordon (B-sine-Gordon) equation, the Boussinesq-double sinh-Gordon equation (B-sinh-Gordon), and the Boussinesq-Liouville (BL) equation are formally derived. The approach rests mainly on the variable separated ODE method. Distinct sets of exact solitary wave solutions, that possess distinct physical structures, are obtained for each equation.