Exact Rational Solutions to A Boussinesq-Like Equation in (1+1)-Dimensions

A Boussinesq-like nonlinear differential equation in (1+1)-dimensions is introduced by using a generalized bilinear differential equation with the generalized bilinear derivatives D3,x and D3,t. A class of rational solutions, generated from polynomial solutions to the associated generalized bilinear equation, is constructed for the presented Boussinesq-like equation. It is conjectured that this class of rational solutions contain all such rational solutions to the new Boussinesq-like equation. More concretely, the conjecture says that if a polynomial f=f(x,t) in x and t solves fttf−ft2+3fxx2=0, then the degree of f with respect to t must be less than or equal to 1.