Solving Equal-width Wave-burgers Equation By (gg)-expansion Method

Abstract

In this paper, we apply the (G'/G)-expansion method to give traveling wave solutions of the third order equal-width wave-Burgers (EW-Burgers) equation. This method is direct, concise and effective and its applications are promising, and it appears to be easier and faster by a symbolic computation system like Maple or Matlab. This work highlights the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.

Soliton solutions of DSW and Burgers equations by generalized (G′/G)-expansion method

“…There is no effective method for solving all varieties of nonlinear equations till now. As a result many powerful and efficient methods have been developed to find exact traveling wave solutions such as, the tanh-method [1][2], the extended tanhfunction method [3], the improved Bernoulli sub-equation function (IBSEF) method [4], the Global Multi-Trace Method [5][6], the extended direct algebraic method [7][8], the (G′/G)expansion method [9][10][11], the extended (G′/G)-expansion method [12], the enhanced (G′/G)expansion method [13][14][15][16], The FD-BPM algorithm [17], the modified F-expansion method [18], the Hirota bilinear method [19][20], the modified simple equation method [21][22][23][24][25][26][27], the simple equation method [28], the complex method [29], the free space radiation mode (FSRM) method [30], the homogeneous balance method [31], the Exp(-Φ(η))-expansion method [32][33][34], the new generalized (G′/G)-expansion method [35][36][37][38], the Adomian decomposition method [39], the sine-cosine method [40] etc. The new generalized 𝐺 ′ /𝐺)eexpansion method is a very impressive, powerful and effective mathematical tool for searc...…”

Soliton solutions of DSW and Burgers equations by generalized (G'/G) -expansion method

“…There is no effective method for solving all varieties of nonlinear equations till now. As a result many powerful and efficient methods have been developed to find exact traveling wave solutions such as, the tanh-method [1][2], the extended tanhfunction method [3], the improved Bernoulli sub-equation function (IBSEF) method [4], the Global Multi-Trace Method [5][6], the extended direct algebraic method [7][8], the (G′/G)expansion method [9][10][11], the extended (G′/G)-expansion method [12], the enhanced (G′/G)expansion method [13][14][15][16], The FD-BPM algorithm [17], the modified F-expansion method [18], the Hirota bilinear method [19][20], the modified simple equation method [21][22][23][24][25][26][27], the simple equation method [28], the complex method [29], the free space radiation mode (FSRM) method [30], the homogeneous balance method [31], the Exp(-Φ(η))-expansion method [32][33][34], the new generalized (G′/G)-expansion method [35][36][37][38], the Adomian decomposition method [39], the sine-cosine method [40] etc. The new generalized 𝐺 ′ /𝐺)eexpansion method is a very impressive, powerful and effective mathematical tool for searc...…”

Kink Soliton Dynamic of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Equation via a Couple of Integration Techniques

“…Researchers have used various solution methods to obtain exact solutions of many important NLPDEs. Some of these methods are the Kudryashov method [1][2][3], tanhcoth method [4][5][6], new Kudryashov method [7][8][9], modified F-expansion method [10,11], extended tanh method [12][13][14][15], generalized projective Riccati equations method [16][17][18], (G /G) expansion method [19][20][21], extended rational sine-cosine method [22][23][24][25], extended Kudryashov method [26][27][28][29], inverse scattering transform method [30], Hirota's bilinear method [31], Darboux transformation [32], the ansatz methods [33] and the Lie symmetry or Lie group method [34].…”