Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey–Stewartson-type equation via a new method

Explicit and Exact Traveling Wave Solutions of Cahn Allen Equation Using 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.…”

Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation

“…Science and engineering problems are generally nonlinear, therefore it is important to generate new efficient methods to solve such nonlinear problems. With the help of computerized symbolic computations, many researchers have implemented various methods to establish the solutions to different nonlinear differential equations e.g., the Exp-function method, the Jacobi elliptic function expansion method, the first integral method, the (G'/G)-expansion method, the direct algebraic method, the Cole-Hopf transformation method [1][2][3][4][5][6][7][8] and others. Fractional differential equations are considered as the general form of the differential equations that involved derivatives of any real or complex order.…”

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.…”