Symmetry Analysis Of Two Kinds Of The Forth-Order Evolution Equations

This paper studies the classical and non-classical symmetries of two Benney equations, obtains the invariant groups, optimal system and the reduced ODEs. In the classical case, we acquire some group-invariant solutions of Benney equation by using the G'/G-expansion method. In the next chapter, we show that some kinds of forth-order evolution equations admit certain types of generalized conditional sym-metries, and as a result, exact solutions to some special equations are obtained. A conclusion is given in the last chapter.