Solitary Wave Solutions for the Sawada-Kotera Equation

İnç, Mustafa; Kılıç, Bülent; Karatas, Esra; Akgül, Ali

doi:10.1166/jap.2017.1318

Cited by 16 publications

(4 citation statements)

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“…Various Investigators have created some other techniques based on Homotopy are HPM [10] , [14] , [15] , [16] , OHAM [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , and Optimal Homotopy Perturbation Method (OHPM) [27] , [28] , [29] , [30] to achieve the solution of BVPs. The new relevant work can also be seen in [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] . Some work about the applied method can be seen in [47] , [48] , [49] , [50] , [51] , [52] , [53] .…”

Section: Introductionmentioning

confidence: 97%

Solutions of nonlinear real world problems by a new analytical technique

Ali

Islam

Gul

et al. 2018

Heliyon

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Here a new analytical scheme is presented to solve nonlinear boundary value problems (BVPs) of higher order occurring in nonlinear phenomena. This method is called second alternative of Optimal Homotopy Asymptotic Method. It converts a complex nonlinear problem into zeroth order and first order problem. A homotopy and auxiliary functions which are consisted of unknown convergence controlling parameters are used in this technique. The unknown parameters are determined by minimizing the residual. Many methods are used to determine these parameters. Here Galerkin's method is used for this purpose. It is applied to solve non-linear BVPs of order four, five, six, and seven. The Consequences are compared with other methods e.g., Differential Transform Method (DTM), Adomain Decomposition Method (ADM), Variational Iteration Method (VIM), and Optimal Homotopy Asymptotic Method (OHAM). It gives efficient and accurate first-order approximate solution. The achieved results are compared with the exact solutions as well as with other methods to authenticate the applied technique. This method is very simple and easy but more operative.

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Section: Introductionmentioning

confidence: 97%

Solutions of nonlinear real world problems by a new analytical technique

Ali

Islam

Gul

et al. 2018

Heliyon

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“…In previous few years, a dynamic research has been carried to investigate soliton solutions of nonlinear equations. Various methods 28‐53 are used to obtain the closed form of wave solutions of different NLEEs. Many researchers endeavored to find the different forms of solutions of Chaffee–Infante equation in (2 + 1)‐dimensions and Zakharov equation like, Sakthivel and Chun 54 examined Chaffee–Infante equation in (2 + 1)‐dimensions to get traveling wave solution by applying exp ‐function method.…”

Section: Introductionmentioning

confidence: 99%

Exact traveling wave solutions of Chaffee–Infante equation in (2 + 1)‐dimensions and dimensionless Zakharov equation

Tahir¹,

Kumar

Rehman

et al. 2020

Math Methods in App Sciences

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In this work, the generalized Kudryashov method is used to obtain the exact traveling wave solutions for two important nonlinear evolution equations, the Chaffee-Infante equation in (2 + 1)-dimensions and the dimensionless Zakharov equation. The generalized Kudryashov method is successfully used for getting exact solutions of these nonlinear equations in the form of exponential function solutions and hyperbolic function solutions. Moreover, we have discussed the dynamical behaviors through graphical representation of the solutions obtained in this way.

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“…Nowadays, e-commerce offers a new and powerful gateway for online shopping. Therefore, online shopping becomes an energy and cost-saving activity that customers have greater choices without geographical constraints (Chuan et al , 2013; Inc et al , 2017; Aghajani and Ghadimi, 2018; Styhre, 2018). For efﬁciently serving the customers, it is important to identify each customer’s specific necessities and recommend a personalized shopping list (Hung, 2005).…”

Section: Introductionmentioning

confidence: 99%

A new model for assessing the role of customer behavior history, product classification, and prices on the success of the recommender systems in e-commerce

Wakil

Alyari²,

Ghasvari

et al. 2019

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Purpose This paper aims to propose a new method for evaluating the success of the recommender systems based on customer history, product classification and prices criteria in the electronic commerce. To evaluate the validity of the model, the structural equation modeling technique is employed. Design/methodology/approach A method has been suggested to evaluate the impact of customer history, product classification and prices on the success of the recommender systems in electronic commerce. After that, the authors investigated the relationship between these factors. To achieve this goal, the structural equation modeling technique was used for statistical conclusion validity. The results of gathered data from employees of a company in Iran is indicated the impact of the customer history on the success of recommender systems in e-commerce which is related with the user profile, expert opinion, neighbors, loyalty and clickstream. These factors positively influence the success of recommender systems in ecommerce. Findings The obtained results demonstrated the efficiency and effectiveness of the proposed model in term of the success of the recommender systems in the electronic commerce. Originality/value In this paper, the effective factors of success of recommender systems in electronic commerce are pointed out and the approach to increase the efficiency of this system is applied into a practical example.

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Solitary Wave Solutions for the Sawada-Kotera Equation

Cited by 16 publications

References 0 publications

Solutions of nonlinear real world problems by a new analytical technique

Solutions of nonlinear real world problems by a new analytical technique

Exact traveling wave solutions of Chaffee–Infante equation in (2 + 1)‐dimensions and dimensionless Zakharov equation

A new model for assessing the role of customer behavior history, product classification, and prices on the success of the recommender systems in e-commerce

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