A new method of exact travelling wave solution for coupled nonlinear differential equations

Exact Traveling Wave Solutions for the (1 + 1)-Dimensional Compound KdVB Equation via the Novel (G'/G)-Expansion Method

“…On the other hand, not all equations posed by the advent of NLEEs models are readily solvable. As a result, many original techniques have been successfully urbanized by various groups of researchers, such as the Cole-Hopf transformation method [1], the Miura transformation method [2], the Hirota's bilinear method [3], the ( ) ( ) exp η −Φ -expansion method [4]- [6], the Sumudu transform method [7]- [14], the Fan sub-equation method [15] [16], the spectral-homotopy analysis method [17] [18], the least-squares finite element scheme [19], the (G′/G)-expansion method [20]- [23], the improved (G′/G)-expansion method [24], the trial function method [25], the nonlinear transform method [26], the extended Tanh-function method [27] [28], and the novel (G′/G)-expansion method [29]- [34], homotopy analysis method [35], to name a few. The latter sequence of papers really constituted a ladder honed in the current wealth of repeated experimental and theoretical successes that sprang us to the work at hand, that we hope will greatly benefit the readership, towards the further understanding of NLEEs dynamics and solutions, and mechanisms for recognizing and classifying them.…”

The (F/G)-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations

“…During the past four decades or so, the many researchers are interested to find powerful and efficient methods for analytic solutions of nonlinear equations. Many powerful methods to obtain exact solutions of nonlinear evolution equations have been constricted and developed such as the inverse scattering transform in [1], the Backlund/Darboux transform in [2][3][4], the Hirota's bilinear operators in [5], the truncated Painleve expansion in [6], the tanh-function expansion and its various extension in [7][8][9], the Jacobi elliptic function expansion in [10,11], the F-expansion in [12][13][14][15], the sub-ODE method in [16][17][18][19], the homogeneous balance method in [20][21][22], the sine-cosine method in [23,24] the rank analysis method in [25], the ansatz method in [26][27][28], the expfunction expansion method in [29] and so on, but there is no unified method that can be used to deal with all types of nonlinear evolution equations. )evolution equation with variable coefficients.…”

Soliton building from spontaneous emission by ring-cavity fiber laser using carbon nanotubes for passive mode locking

“…Many articles have been published on the exact solutions to nonlinear wave equations. These include studies of the Backlund transform, 29 the hyperbolic tangent expansion method, 30 the trial function method, 31 the nonlinear transform method, 32 transformed rational function method, 33 and exact 1-soliton solution of the complex modified Korteweg-de Vries equation method. 34 Numerical methods, such as the split-step Fourier method, have become popular with the development of computing capabilities, although they only give approximate solutions of the NLS equation.…”