Abstract
The recursion operator of a new modified KdV equation and its inverse are explicitly given. Acting the recursion operator and its inverse on the trivial symmetry 0 related to the identity transformation, the infinitely many local and nonlocal symmetries are obtained. Using a closed finite dimensional symmetry algebra with both local and nonlocal symmetries of the original model, some symmetry reductions and exact solutions are found.
Highlights
The symmetry study plays an important role in almost all the scientific fields, especially, in mathematical physics
Lou pointed out that the infinitely many nonlocal symmetries can be constructed via acting the inverse recursion operator on the identity transformation [1], infinitely many Lax pairs [2], Darboux transformations [3], Backlund transformations [4], conformal transformations [5], and so on
We have studied the symmetries and symmetry reduction solutions of a new modified KdV equation proposed by Lou
Summary
The symmetry study plays an important role in almost all the scientific fields, especially, in mathematical physics. To find infinitely many symmetries of a given integrable model, one of the best ways is to construct a recursion operator of the studied model. Lou pointed out that the infinitely many nonlocal symmetries can be constructed via acting the inverse recursion operator on the identity transformation [1], infinitely many Lax pairs [2], Darboux transformations [3], Backlund transformations [4], conformal transformations [5], and so on. To study different physical phenomena, there exist some different versions of the modified KdV models such as the Gardner equation (the combination of the KdV and the mKdV systems) and the Wadati equations.
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