Abstract
In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form. Also this system was found as a special case of the four-reduction of the Kadomtsev-Petviashivilli hierarchy. We obtain exact solutions of the system by using Lie symmetry analysis along with the simplest equation and Jacobi elliptic equation methods. Also, symmetry reductions are obtained based on the optimal system of one-dimensional subalgebras. In addition, the conservation laws are derived using two approaches: the new conservation theorem due to Ibragimov and the multiplier method.
Highlights
In recent years many nonlinear evolution equations (NLEEs) have been used to model many real world problems in various fields of science and engineering
It is true that finding solutions of NLEEs is a difficult task, and only in few special cases one can write down the explicit solutions
Some of the most important methods found in the literature include the ansatz method [, ], the Weierstrass elliptic function expansion method [ ], the Darboux transformation [ ], Hirota’s bilinear method [ ], the (G /G)-expansion method [ ], the Jacobi elliptic function expansion method [, ], the inverse scattering transform method [ ], the homogeneous balance method [ ], the Bäcklund transformation [ ], the F-expansion method [ ], the exp-function method [ ], the multiple expfunction method [ ], the variable separation approach [ ], the sine-cosine method [ ], the tri-function method [, ], and the Lie symmetry method [ – ]
Summary
In recent years many nonlinear evolution equations (NLEEs) have been used to model many real world problems in various fields of science and engineering. The simplest equation method [ ] and the Jacobi elliptic function method [ ] are later employed to obtain some exact solutions of ( ).
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