The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation

On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

“…Substituting ( 9) in ( 8) and equating the coefficients of each polynomial of Φ( ) to zero, we obtain the set of algebraic equations in w 0 , w 1 , n , m, and Θ. Solving obtained set of equations, we get 2 . The family of solutions of (6) corresponding to Equations ( 7), (9), and (10) are obtained: Family 1: When Θ 2 − 4 < 0 and ≠ 0, then the periodic-singular solutions are:…”

“…The construction of mathematical models for real-world phenomena and improvement of useful methods to define them is one of the most important field in applied mathematics. Many analytical methods for studying such kind of problems have been developed by researchers from all over the world such as the sine-cosine method, 1 modified extended tanh-function method, 2 the extended and improved F-expansion method, 3 the homogenous balance method, 4 the Hirota's bilinear method, [5][6][7][8][9] the inverse scattering method, 10 the Backlund transformation method, 11,12 truncated Painleve expansion method, 13 the variational method, 14 He's semi-inverse variational principle, 15 the asymptotic method, 16 the method of integrability, 17 homotopy perturbation method, 18 the soliton perturbation theory, 19 the Sine-Gordon expansion method, 20 generalized Darboux transformation method, 21 the Kudryashov's method, 22 the Sardar-subequation method, 23 the modified extended direct algebraic method (EDAM), 24 the mapping method, 25 and tanh method. 26 In addition, a huge interest has been revealed in the field of fractional calculus.…”

Multiple Exact Travelling Solitary Wave Solutions of Nonlinear Evolution Equations

“…However, the class of this NLPDE when 0   is considered in [19]. This paper is organized to fully present the algorithm of the considered method in Section 2.…”

Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics

“…Physicists, engineers and mathematicians have established precise solutions for the NLEEs that transform into a key task in the analysis of nonlinear physical incidents. Generally, there is no single approach to resolve all sorts of NLEEs, and a variety of scientific groups have successfully established many techniques, including the method of extended tanh-function [1], the method of tanh function [2,3], the method of sine-cosine [4], the method of modified extended tanh function [5], the method of exp (−ϕ(ξ ))-expansion [6], the method of exp-function [7], the method of Backlund transformation [8], the method of Miura transformation [9], the method of extended F-expansion [10], the method of improved F-expansion [11], the method of ( ′/ / G G G , 1 )-expansion [18], the method of (G′/G)expansion [12][13][14][15], the method of new auxiliary equation [16], the method of auxiliary equation [17], the method of Kudryashov [18][19][20][21], the method of modified Kudryashov [29], the method of extended trial function [31], the method of variational iteration [32], the method of modified simple equation (MSE) [22][23][24][25][26][27][28][29][30][31][32], extended modified direct algebraic method, extended mapping method and Seadawy techniques to find solutions for some nonlinear partial differential equations [33][34]…”