The (G`/G)-Expansion Method for Traveling Wave Solutions of Burgers’ Kdv and Generalization of Huxley Equations

Abstract

The (G`/G)-expansion method is used for determining the exact traveling wave solutions of the Burgers-KdV and generalization of Huxley equations. The obtained solutions are compared with the solutions found by Wazwaz[18]. The (G`/G)-method is very powerful and easy tool for solving non-linear partial differential equations

On Some Complex Aspects of the (2+1)-dimensional Broer-Kaup-Kupershmidt System

“…Nonlinear evolution equations often used to describe complex aspects in the field of nonlinear sciences such as Biological sciences, chemistry, mathematical physics, engineering and physics. For the past decades, various scholars have displayed their different effort for seeking the solutions of such types of equations, many analytical methods have been developed for this task such as sine-Gordon expansion method [1][2][3], the Bell-polynomial method [4], the new generalized Jacobi elliptic function expansion method [5], the Exp-function method [6], the modified Exp-function method [7], the (G /G)-expansion method [8][9][10], the sub equation method [11], the simplified Hirota's method [12], the simplest equation method [13], the modified simplest equation method [14][15][16], the improved (G /G)-expansion method [17], the multiple exp-function algorithm [18], the Lie group analysis and symmetry reductions [19]. In general, various methods have been developed to explore the search of different types of solutions to different kind of NLEEs [20][21][22][23][24][25][26].…”