Lie-B¨acklund Transformations and Symmetries approach to exactly solvable evolution For Soliton Equation
In this paper, we obtain well-known B¨acklund transformations of several equationsv by applying Symmetries methods . We indicate by examples how symmetries of a system of differential equations . Also, these equations may be combined with a B¨acklund map for the system to produce another B¨acklund map. Finally we show that one can obtain Symmetries of Soliton equations from their B¨acklund Transformations.We explain briefly the conceptsof LB trasformation group,infinitesimal LB symmetries and the associated evolution equations and the methods of obtaining them.
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