An innovative approach for developing the precise traveling wave solutions to a family of 3D fractional WBBM equations

Dynamical behavior of water wave phenomena for the 3D fractional WBBM equations using rational sine-Gordon expansion method

“…Simply put, it employs a more structured technique and more steps to generate an algebraic system. It also automatically creates kink and singular soliton solutions 17 – 19 . The principal important methodology of this method is too explicit the exact solutions of FNLEEs that satisfy the Nonlinear ODE of the form, .…”

“…Heat flow, shallow water waves, wave propagation, optical fibres, plasma physics, fluid mechanics, biology, electricity, chemical kinematics, and quantum theory are only a few examples of the numerous nonlinear wave techniques that have been employed in the past to illustrate different physics issues 22 – 24 . Thus, to investigate these substances, scores of effective strategies have been recommended in the circulated works by scholars, namely the improved modified extended tanh-function method 17 , the (G′/G,1/G)-expansion technique 15 , 25 , the modified extended tanh-function method 8 , 26 , 27 , the (Gʹ/G 2 )-expansion technique 16 , 28 , the advanced exp(− ∅(ξ))-expansion method 29 – 31 , the tanh-coth method 32 , the variational iteration method 33 – 35 , the method of characteristics 36 , the exp function method 37 , the sine-Gordon expansion method 18 , Wang's Bäcklund transformation-based method 38 , the new auxiliary equation method 19 , the Hirota bilinear method 39 – 41 , Soret and Dufour effects 42 , Variational method 43 , Deep Learning approach 44 , Dixon resultant method 45 , the three-dimensional molecular structure model 46 , the Kudryashov method 47 , etc.…”

Rational Sine-Gordon expansion method to analyze the dynamical behavior of the time-fractional phi-four and (2+1) dimensional CBS equations

“…-. Mamun et al, 2022), the (G′/G,1/G)expansion technique (Alam et al, 2021b;Mamun et al, 2021b), the modified extended tanhfunction method (Alam et al, 2021a;Mamun et al, 2021aMamun et al, , 2020, the (G ′ /G 2 )-expansion technique (Ananna et al, 2021;Mamun et al, 2021c), the advanced exp(−∅(ξ))-expansion method (A. Al Mamun et al, 2022a;Shahen et al, 2021Shahen et al, , 2020, the tanh-coth method (A. Al Mamun et al, 2022b), the variational iteration method (Al---- Mamun et al, 2019;Al-Mamun and Asaduzzaman, 2019;Ananna and Al -Mamun, 2020), the method of characteristics (Ali and Miah, 2018), the exp function method (Rahmatullah et al, 2018), the sine-Gordon expansion method (A. Al Mamun et al, 2022c), Backlund transformations (Ma and Fuchssteiner, 1996), the new auxiliary equation method (Mamun et al, 2023), transformed rational function method (Ma and Lee, 2009a), Hirota bilinear forms (Ma and Zhou, 2018), the generalized Hirota bilinear method (Huang et al, 2021), Soret and Dufour effects (Gharami et al, 2022), Bifurcation theory (Li et al, 2022), Deep Learning approach (Liu et al, 2020), Dixon resultant method (Qin et al, 2022), the three-dimensional molecular structure model (Qing et al, 2022), the Kudryashov method (Chen et al, 2022), etc.…”

Dynamical behavior of water wave phenomena for the 3D fractional WBBM equations using rational Sine-Gordon expansion method

“…Backlund transformations [37], the new auxiliary equation method [38], transformed rational function method [39], Hirota bilinear forms [40], the generalized Hirota bilinear method [41],…”