Application of G'/G expansion method to two concert problems

Abstract

In this work G G  -expansion method is used to obtain exact solutions of the Jimbo-Miwa (JM) and TzitzeicaDodd_Bullough (TDB) equations. It is shown that G G  -expansion method is straightforward and concise, and its applications are promising.

Auto-Backlund transformations and New Exact Soliton Solutions of KdV Equation for Nonlinear Dust Acoustic Solitary Waves in Dust Plasma with Variable Dust Charge

“…We use the reductive perturbation technique to derive a KdV equation. would like to use the homogeneous balance method [15,16] to construct an auto-Bäcklund transformation (BT) [17][18][19][20][21][22][23] , new exact soliton solutions of KdV equation are obtained and we have applied the modifiedǴ G expansion method [24][25][26][27][28][29][30][31], the sine-cosine expansion method, the sinh-coshine expansion method ,and the sech-tanh expansion method [33,[37][38][39][40][41] and to obtain a new travelling wave solutions of KdV equation. The paper is organized as follows :This introduction in Section 1.…”

Invariance of Painlevé property for some reduced (1+1)-dimensional equations

“…(3). Ayati and Biazar [15] derived the generalized solitary solutions to Eq. ( 3) with exp-function method.…”