Travelling wave solutions of the Cahn–Allen equation by using first integral method

Many Families of Exact Solutions for Nonlinear System of Partial Differential Equations Describing the Dynamics of DNA

“…Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. Because of the increased concentration in the theory of solitary waves, a large variety of analytic and computational methods have been established in the analysis of the nonlinear models (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). An attractive nonlinear model for the nonlinear science is the deoxyribonucleic acid (DNA).…”

On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

“…Raslan [16] has used this method for the Fisher equation. Tascan and Bekir [17] have used this method for the Cahn-Allen equation. Abbasbandy and Shirzadi [18] have investigated the Benjamin BonaMohany equation by this method.…”

Explicit and Exact Traveling Wave Solutions of Cahn Allen Equation Using MSE Method

“…Most of the above methods are dependent on computational software except the MSE method. The objective of this paper is to look for new exact traveling wave solutions includingtopological soliton, single soliton solutions of the well-recognized Cahn-Allen equation [30,31] viathe MSE method.…”

“…Advanced nonlinear techniques are importantfor solving inherentnonlinear problems, particularly those involving dynamicalsystems and allied areas. In recent years, there have beenbigimprovements in finding the exact solutions of NLEEs.Many powerful methods have been establishedand enhanced, such as the modified extended Fan sub-equation method [1], the homogeneous balance method [2,3], the Jacobi elliptic function expansion [4], the Backlund transformation method [5,6], the Darboux transformation method [7],the Adomian decomposition method [8][9], the auxiliary equation method [10,11], the ( / ) G G ′ -expansion method [12][13][14][15][16][17][18], the Exp-( ( )) −φ ξ -expansion method [19], the sine-cosine method [20][21][22], the tanh method [23],the F-expansion method [24,25], the exp-function method [26,27],the modified simple equation method [28][29][30],the first integral method [31], the simple equation method [32], the bilinear method [33], the transformed rational function method [34],and so on. Most of the above methods are dependent on computational software except the MSE method.…”