Calculating Symmetries And Invariant Solutions Of A Several Kinds Of Evolution Equations By Wu's Method

We calculated potential symmetries and invariant solutions of three evolution equations-BBM-Burgers equation, Benjanmin Ono equation and NTT equation by differential form Wu's method in this paper.1. we first calculated characteristic set of determining equations satisfied by the generate functions (infinitesimal) of the symmetries, then solved the corresponding equations of the characteristic set by using ascending set (triangulated) structure of the characteristic set and the relation between zero set of characteristic set and solution set of the original determining equations. This process significantly simplifies procedure of solving over-determined determining equations.2. we calculated classical symmetries of the three kinds of the evolution equations, and solved corresponding some invariant solutions.3. we calculated potential symmetries of the three equations by using their first and second conserved form. Then we compared the potential symmetries with classical symmetries. Under same condition on constant appeared in equation, we obtained some potential symmetries (new symmetries). It provides the possibility for widely solving invariant solutions of these equations.4. we generated a series new exact solutions of the three kinds of evolution equations by applying different symmetries on a invariant solutions of a specific symmetry. This has provided a new way for obtaining exact soultions of a given partial differential equations (PDEs).5. we gave symmetries commutator table, and showed the algebra relations among the symmetries. 6. we gave corresponding global groups for some potential symmetries.