The Klein–Fock–Gordon and Tzitzeica dynamical equations with advanced analytical wave solutions

Stable and functional solutions of the Klein-Fock-Gordon equation with nonlinear physical phenomena

“…To the skilled of our knowledge, applying the generalized Kudryashov method and the modified expansion method to the KFG has not been published earlier. Here, comparing our secured answers including Seadawy et al solutions in [34]. Seadawy et al [34] obtained only eight solutions through the extended simple equation method and twelve solutions through the modified F-expansion method.…”

“…Here, comparing our secured answers including Seadawy et al solutions in [34]. Seadawy et al [34] obtained only eight solutions through the extended simple equation method and twelve solutions through the modified F-expansion method. We received twenty solutions of the studied model through the modified (G′/G)-expansion method and six solutions of the same model through the generalized Kudryashov method.…”

“…-expansion method [9,10], novel (G′/G)-expansion method [11,12], nonlinear adaptive control scheme [13], the unified method and its generalized form [14][15][16][17], Linear non-adaptive boundary control law [18,19], the improved Bernoulli sub-equation function method [20], tanh-coth expansion method [21], rational sine-cosine method [22], the sine-Gordon expansion method [23,24], the enhanced modified simple equation method [25], the exponential rational function method [26], the simplified Hirotas method [27], Darboux transformation method [28], N-fold Darboux transformation [29], Lie symmetry approach [30], the power index method [31], generalized Kudryashov method [32], novel operational method [33], extended simple equation [34], (G′/G)-expansion method [35], the extended sinh-Gordon equation expansion method [36,37], the Hirota bilinear approach [38,39], the extended rational sinecosine and rational sinh-cosh methods [40], new extended rational SGEE method [41], the extended unified method [42,43] and many other approaches.…”

Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

“…Furthermore, a technologically advanced scheme in [48] utilized the three wave method to obtain some exact solutions for Equation (1). To the best of our understanding, Equation (1) has not been studied with our implemented mathematical methods, see details in [49][50][51].…”

The influence of the differential conformable operators through modern exact solutions of the double Schrödinger-Boussinesq system

“…Such as solid state physics, fluid mechanics, quantum physics, plasma physics, optics, statistical physics, and so on [5][6][7]. Moreover, the exact wave solutions of the NES can be extracted and analyzed by plentiful valuable schemes, like the general ¢ -G G expansion ( ) scheme [8,9], the improved simple equation scheme [10], the first integral scheme [11], the Exp-function scheme [12], the F-expansion scheme [13], Lie symmetry analysis [14,15] and others. Particularly, Kudryashov [16] has succeeded in introducing an effective and handy scheme for constructing solitary and periodic wave solutions to the NES.…”