Non-classical symmetry and new exact solutions of the Kudryashov-Sinelshchikov and modified KdV-ZK equations

Document Type : Original Article


Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran


‎In this paper‎, ‎by applying the non-classical symmetry method‎, ‎non-classical symmetries of the Kodryashov-Sinleschikov (K-S) and‎ ‎modified Korteweg-de Vries-Zaharov-Kuznetsov (mKdV-ZK) equations are‎ ‎obtained‎. ‎Apart from classical symmetries‎, ‎this theory can be‎ ‎effective in finding a few other solutions for a system of PDEs and‎ ‎ODEs‎. ‎Also‎, ‎non-classical symmetries of a system of PDEs can be‎ ‎applied to reduce the number of independent variables‎. ‎By adding the‎
‎invariance surface condition to the assumed equations and applying‎ ‎the classical symmetry method for them‎, ‎non-classical symmetries are‎ ‎calculated‎. ‎Finally‎, ‎some of the group invariant solutions and the‎ ‎similarity reduced equations associated to non-classical symmetry‎ ‎are obtained‎.


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