By the homogeneous balance method,we obtain a series of exact wave solutions for the real quintic Swift-Hohenberg(RQSH) equation,including solitary wave solutions,kink wave solutions,periodic wave solutions,and singular kink wave solutions.

The existence of smooth solitary wave solutions,kink and antikink wave solutions and periodic wave solutions are proved.

By using the bifurcation theory of dynamical systems to third-order nonlinear Schrdinger equation,the smooth solitary wave solutions,kink and anti-kink wave solutions and periodic wave solutions are obtained.

By finding parabola solutions to a planar dynamical systems connecting two equilibrium points, the existence of the kink wave solutions and their exact parametric representations are obtained for a Type of Nonlinear Evolution Equation.

Exact explicit parametric representations of kink and anti-kink wave solutions,periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given.

By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations was shown.

Exact explicit parametric representations of kink and anti-kink wave solutions,periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given.

By using the theory of bifurcations of dynamical systems to a system of coupled nonlinear equations,kinkwave solutions and anti-kink wave solutions are obtained.

Under various parameter conditions,all explicit formulas of solitary wave solutions and kink wave solutions are obtained.

The Kink Waves of A Boussinesq Quartic Equation;