Frobenius integrable decompositions of nonlinear evolution equations with modified term

Frobenius integrable decompositions are introduced for nonlinear evolution equations with modified term. Two classes of polynomial equations with modified term are transformed into Frobenius integrable ordinary differential equations by two special Bäcklund transformations. The resulting solutions are illustrated to describe the solution phenomena shared with the mKdV equation, Sharma-Tasso-Olver equation, the modified Kawachara equation, the fifth-order KdV equation and its various forms.