Homoclinic Bifurcation for Boussinesq Equation with Even Constraint

The exact homoclinic orbits and periodic soliton solution for the Boussinesq equation are shown. The equilibrium solution u₀=-1/6 is a unique bifurcation point. The homoclinic orbits and solitons will be interchanged with the solution varying from one side of -1/6 to the other side. The solution structure can be understood in general.