الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Different approaches have been presented for finding invariants of
some nonlinear partial differential equations (POEs). In these
approaches, invariants are found by using free parameter method III,
separation of variables method (21. bTfOUP properties for differential
equations 13,41. and dimensional analysis for finding the invariants 151.
Obtaining invariant solutions reduce to solving quotient
differential equations in fewer independent variables than the original
equations. In particular, These quotient equations might be ordinary
differential equations (ODEs).
The motivation of this work is to apply a method called the
similarity method 110t only to find invariants of nonilinear POEs but
also to predict the existance of invariants (this method essentially dates
back to the original investigations of Sophus Lie (6-81). By this method,
one can try to obtain invariant, partially invariant solution to perform
the group, to transform a given POE to a less complicated or ODE via
one-parameter Lie 1!fOUP of transformations 14,5,91.
This method IS used to the nonlinear PDEs which describe some
nonlinear physical problems in order to construct all possible classes of
similarity solutions and to give a strong group-theoretical classification
of the results. These classes of solutions can be obtained and classified
hy means of the similarity method if the group constants allowed to
take some special values. Besides these known classes of solutions the
method is shown 10 create additional classes of similarity solutions
heretofore undiscovered. We wish to remark that the similarity method
may be called to play all interesting role in nonlinear mechanics.