The ()-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics

Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

“…When a NLEE is analysed, one of the most important question is the construction of the exact solutions for equation [1]. In the open literature, quite a few methods for obtaining explicit travelling and solitary wave solutions to NLEEs have been suggested such as the inverse scattering method [2], the bilinear transformation method [3], the tanh-sech method [4,5], the extended tanh method [6,7], the sine-cosine method [8][9][10], the homogeneous balance method [11,12], the pseudo spectral method [13], the G ′ /G -expansion method [14][15][16], exp-function method [17], variational iteration method [18], homotopy perturbation method [19], the Jacobi elliptic function method [20], Lie group analysis method [21] and so on.…”

Exact Solutions for the Nonlinear PDE Describing the Model of DNA Double Helices using the Improved (G′/G)- Expansion Method

“…With the development of solitary theory many powerful methods for obtaining the exact solutions of the nonlinear evolution equations are presented and can be found in Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. An attractive nonlinear model of the nonlinear science is the deoxynbonucleic acid (DNA).…”

“…The objective of this article is to apply the improved (G ′ /G)-expansion method to find many exact traveling wave solutions of the model (1), namely the hyperbolic, trigonometric and rational function solutions. Comparison between some of our new results and the well-known results obtained in [31] will be given later.…”

“…2 Derivation of the model of DNA double helices (1) With reference to [31], the helical axis for the Watson-Crick model of DNA is taken in the x-direction. The base and its complementary base may vibrate each other along the direction of hydrogen bonds in a base pair.…”

Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity

“…Wang et al [32], the (G /G)-expansion method was very well received and a number of studies refining the initial idea appeared in the research literature [33][34][35]. The basic idea of the (G /G)-expansion method lies in the fact that it takes full advantage of linear theory.…”