2013
DOI: 10.1063/1.4804433
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Extended generalized Riccati equation mapping method for the fifth-order Sawada-Kotera equation

Abstract: This article was published in the AIP Advances [© 1998 ] and the definite version is available at : http://dx.doi.org/10.1063/1.4804433 The Journal's website is at: http://scitation.aip.org/content/aip/journal/adva/3/5/10.1063/1.4804433In this article, the generalized Riccati equation mapping together with the basic (G′/G)-expansion method is implemented which is advance mathematical tool to investigate nonlinear partial differential equations. Moreover, the auxiliary equation G′(φ) = h + f G(φ) + g G 2(φ) is… Show more

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Cited by 23 publications
(10 citation statements)
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“…Let us define the general solution in the polynomial form of (36)-(37). For further details, see [20,28,29]:…”
Section: Generalized Riccati Equation Mapping (Grem) Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Let us define the general solution in the polynomial form of (36)-(37). For further details, see [20,28,29]:…”
Section: Generalized Riccati Equation Mapping (Grem) Methodsmentioning
confidence: 99%
“…The different numerical schemes include the forward Euler difference scheme [13], the non-standard finite difference scheme [14], the backward Euler difference scheme [15], the implicit finite difference scheme [16], the Crank-Nikolson finite difference scheme [17], etc. On the other hand, to find exact solutions many analytical techniques are used to explore exact solutions for nonlinear PDEs, such as the new modified extended direct algebraic method [18], the G ′ /G-model expansion method [19], the Riccati equation mapping method [20], the Hirota bilinear method [21,22], the modified exponential rational function method [23], and the ϕ 6 -model expansion method [24].…”
Section: Introductionmentioning
confidence: 99%
“…In [35], the modified simple equation is employed to study the problem. In [36], the extended generalized Riccati equation mapping method is adopted to find the exact solutions. Three different effective methods, the extended simplest equation method, modified Kudryashov method and sech-tanh expansion method, are applied in [37].…”
Section: Introductionmentioning
confidence: 99%
“…For example of these methods, the Hirotaʼs bilinear transformation method (Zhou and Ma 2017), the Backlund transform method (Arnous et al 2015), the inverse scattering method (Ablowitz and Musslimani 2016), the first integral method (Tascan and Bekir 2010), the exp-function method (Ma et al 2010), the tanh-function method , Abdel et al 2011, the Jacobi elliptic function method (Ma et al 2018), the ¢ ( ) G G -expansion method (Bekir and Guner 2013;Bekir and Cevikel 2009), the extended ¢ ( ) G G -expansion method (Roshid et al 2014, Alam andBelacem 2015), the improved ¢ ( ) G G -expansion method (Redi et al 2018), the new generalized ¢ ( ) G G -expansion method (Alam 2015, Alam and Stepanyants 2016, Alam and Li 2019, the generalized and improved ¢ ( ) G G -expansion method(Akbar et al 2012aG -expansion method(Akbar et al , 2012b. The Weierstrass elliptic function method (Ping and Li 2008), the truncated Painleve expansion method (Radha et al 2007), the functional variable method (Khan and Akbar 2014), the j x -( ( )) exp -expansion method (Alam and Belacem 2016; Khater 2016, Alam and Tunc 2016, Alam and Alam 2017, the modified simple equation method (Roshid and Roshid 2018), the auxiliary equation method (Kaplan et al 2015, Akbulut et al 2016, the rational exponential function method (Roshid and Alam 2017), the homotopy perturbation method (Javeed et al 2019), the Riccati equation mapping method (Naher et al 2013), the ¢ ( ) G G G , 1 -expansion method (Kaplan et al 2016), etc.…”
Section: Introductionmentioning
confidence: 99%