Summary: With the aid of transformation of the unknown function, a class of nonlinear nonintegrable wave equations is reduced to a trilinear homogeneous equation which can be easily solved. Therefore the exact kink shape solitary wave solutions, singular travelling wave solutions, and the periodic triangle function wave solutions are obtained. As special cases, aBurgers equation, Burgers-Huxley equation, Chaffee-Infante reaction-diffusion equation, Newell-Whitehead equation, FitzHugh-Nagumo equation, and an isothermal autocatalytic system equation can also be solved by this method.