Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

“…The solutions of (4) corresponding to (27), along with solution (10) are Case I: If c−µ k λc > 0 and ρ = 0 then…”

“…Exact solutions produce corporal information to describe the physical behavior of system connected with these NLEs. In recent years, several efficient methods including method of extended tanh [1,2], tanh-coth [3,4], Hirota's direct [5,6], sine-cosine [7,8], extended direct algebraic [9,10], extended trial approach [11,12], Exp [-ϕ(ξ)]-Expansion [13,14], a new auxiliary equation [15,16], Jacobi elliptic ansatz [17,18], generalized Bernoulli sub-ODE [19,20], functional variable [21,22], sub equation [23,24], and so on [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], have been established for efficient solutions of NLEs.…”

Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes

“…So, finding the exact and numerical solutions of these model have been being attracted the attention of many researchers in various branches of science. Consequently, a variety of practical, accurate solution methods have been being developed to be used for solving LPDEs, such as the auxiliary equation method [11,12], the Jacobi elliptic function expansion method [13,14], the (G /G)expansion method [15,16], the modified Kudryashov method [17,18], the first integral method [19,20], the new extended direct algebraic method [21,22], the sine-Gordon expansion method [23,24], the Khater method [25,26], the sub-equation method [27,28], the extended sinh-Gordon equation expansion method [29,30] and so on.…”

New optical explicit plethora of the resonant Schrodinger’s equation via two recent computational schemes

“…Marvellous applications in the field of science and engineering have been formulating in non-linear PDE with an-integer order or fractional order [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Thus, many researchers in different fields have been focusing on studying the exact travelling and solitary wave solutions.…”

“…These solutions are used to discover more physical, dynamical behaviour, and the nature of non-linear problems and explain the different scientific non-linear phenomena. For achieving to this fundamental goal, many computational and numerical schemes have been being formulated such as the improved and novel expansion method [1][2][3], extended simplest equation method [4][5][6][7], first integral method [8,9], Khater method which is derived by Khater in 2017 [10][11][12][13], the exp -expansion method [14,15], the Kudryashov method [16], the Jacobi elliptic functions [17,18], the modified Khater method, [19][20][21][22], the generalized Kudryashov method [23,24], the new extended direct algebraic method [25], the functional variable method [26], Adomian decomposition method [27][28][29], and the sub equation method [30].…”