Soliton solutions of coupled systems by improved (Gʹ/G)-expansion method

New solitary wave solutions of Maccari system

“…Many authors have used to find exact solutions a lot of methods of Maccari system such as exp À ΦðξÞ À Á Àexpansion method, extended F-expansion method, projective Ricatti equation method, first integral method, the tanh-coth method, the sech-csch method, the sec-tan ansatz method, the rational sinh-cosh ansatz method, G 0 =G À Á Àexpansion method, mapping method, lie symmetry approach, He's semi-inverse method, exp-function method, Kudryashov method, the modified simplest equation method, the extended homogeneous balance method, bifurcation theory, extended sine-Gordon equation method, variable separation approach, sine-cosine method and the generalized algebraic method (Maccari, 1996;Rostamy et al, 2011;Jabbari et al, 2011;Zhao, 2008;Zhang, 2007;Wazwaz, 2012;Rostamy and Zabihi, 2012;Abdou et al, 2012;Bekir, 2009;El-Ganaini, 2012;Ye and Zhang, 2011;Manafian and Zamanpour, 2013;Lee and Sakthivel, 2013;Akbari, 2013;Kumar and Chand, 2013;Malik et al, 2012;LiNa and Qing, 2005;Jun-Ting and Lun-Xun, 2007;Huang et al, 2007;Mirzazadeh, 2015;Ahmed et al, 2013;Hafez et al, 2015;Mohyud-Din and Shakeel, 2013).…”

Novel Soliton Solutions of the Fractional Riemann Wave Equation via a Mathematical Method

“…where a 0 , a 1 , and a 2 are unknown parameters to be calculated thereafter. Inserting Equation (18) with Equation (10) into Equation ( 17) and considering every coefficient of (G /G) j as equal to zero, there exist a set or sets of equations (these are not included here for the sake of ease) for a 1 , a 2 , a 3 , and µ with the assistance of CAS, and we obtain: 1st Solution Set:…”

“…Researchers have increasingly concentrated on analytical and numerical solutions to NLFPDEs [6][7][8][9][10][11] with the help of computer science and symbol-based software. Numerous robust computational techniques have been developed in the literature to explore the various types of exact solutions of NLFPDEs, such as the extended rational sinh-cosh method [12], extended tanh-coth method [13], exp-function method [14,15], fractional Riccati expansion method [16], generalized Kudryashov approach [17], enhanced and generalized (G'/G)-expansion scheme [18,19], and Painleve Property [20].…”

On the exact solutions to some system of complex nonlinear models

“…Several attempts by different scientists have been made to investigate Eq. (1.2) [64][65][66][67][68][69][70][71].…”