We introduce a new subgroup embedding property, namely S*-embedded and study the structure of finite group G under assumption that some subgroups prime order are in G. A serie known results unified extended.

In this present study the double layers structure model of extended Korteweg-de Vries(K-dV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma model. Then by using of new analytical method we obtain the new exact solitary wave solutions of this equation. Double layer is a structure in plasma and consists of two p...

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have ...

In this paper, we propose a new extended (G′/G)-expansion method to construct exact traveling wave solutions for nonlinear evolution equations. To check the validity and effectiveness of our method, we implement it to the (2+1)-dimensional typical breaking soliton equation.The results that we get are more general and successfully recover most of the previously known solutions which have been fo...

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...

We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type G2 extending the celebrated T -system relations of type G2. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G2. We use this result to obtain explicit...