Document Type : Original Article

**Authors**

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

**Abstract**

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.

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.

**Keywords**

- Non-classical symmetry
- Invariance surface condition
- Lie invariants
- Reduced equations
- K-S and modified KdV-ZK equation

**Main Subjects**

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March 2023

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