2018
DOI: 10.1088/2399-6528/aaa3a5
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On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method

Abstract: In this paper, the external trial equation method is employed to solve new coupled Konno-Oono (CKO) equation. By using this method, new exact solutions involving parameters, expressed by generalized hyperbolic and elleptic solutions are obtained. The current method presents a wider applicability for handling nonlinear wave equations. In addition, explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and ellip… Show more

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Cited by 18 publications
(12 citation statements)
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References 47 publications
(50 reference statements)
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“…e expressions in ( 27) and ( 28) are new hyperbolic function solutions of conformable time-fractional coupled Konno-Oono equation ( 2) and are given geometrically in Figures 7 and 8, respectively. When α approaches to one, the solutions ( 27) and ( 28) will reduce to a well-known solution for time-integer derivatives coupled Konno-Oono equation ( 2) [27,31,32]. Notice, as outlined in Figures 7(d) and 8(d), the fractional-order derivative influences the Shap of the solitary wave solutions.…”
Section: E Solitary Wave Solutions If (C H)mentioning
confidence: 90%
See 1 more Smart Citation
“…e expressions in ( 27) and ( 28) are new hyperbolic function solutions of conformable time-fractional coupled Konno-Oono equation ( 2) and are given geometrically in Figures 7 and 8, respectively. When α approaches to one, the solutions ( 27) and ( 28) will reduce to a well-known solution for time-integer derivatives coupled Konno-Oono equation ( 2) [27,31,32]. Notice, as outlined in Figures 7(d) and 8(d), the fractional-order derivative influences the Shap of the solitary wave solutions.…”
Section: E Solitary Wave Solutions If (C H)mentioning
confidence: 90%
“…In [23], the tanh-function method and extended tanh-function method have been applied to construct soliton solutions for system (3). Additional methods have been forced such as a new generalized (G′/G)−expansion method [24], the modified exp(−Ω(ξ))− expansion function method [25], the sine-Gordon expansion method [26], the external trial equation method [27], the generalized exp-function method [28], a modified extended exp-function method [29], the extended simplest equation method [30], the extended Jacobian elliptic function expansion method [31], the functional variable and the two variables (G ′ /G, 1/G)− expansion methods [32], and a new extended direct algebraic method [33]. Recently, some techniques have been imposed such as a generalized (G ′ /G)− expansion method for stochastic Konno-Oono equation that is forced by multiplicative noise term [34] and a unified solver with the aid of probability function distributions [35], for more details about wave solutions for stochastic PDE (see, e.g., [36][37][38]).…”
Section: Introductionmentioning
confidence: 99%
“…Recently, this model has attracted a special attention and has been the subject of many studies, such as the ETEM [27], tanh function and extended tanh function methods [28], sine-Gordon expansion approach [29], new extended direct algebraic approach [30], modified simple equation method [31], and extended exp-function method [16].…”
Section: Introductionmentioning
confidence: 99%
“…Expansion [11,15], Generalised Exp-function [16], Extended direct algebraic [17], External trial equation [18], Sine-Gordan expansion [19], Modified exp-Ω(ξ) expansion function [20] and nonlinear analysis [21] etc. are employed to solve different forms of the CKOEs (1).…”
Section: Introductionmentioning
confidence: 99%