In their recently published article, Guner and Atik apply the exp-function method to derive solitary solutions to fractional-order nonlinear differential equations. We argue that the solutions provided by Guner and At...
详细信息
In their recently published article, Guner and Atik apply the exp-function method to derive solitary solutions to fractional-order nonlinear differential equations. We argue that the solutions provided by Guner and Atik do not satisfy the considered equations. Furthermore, we derive correct solitary solutions as well as necessary and sufficient conditions for the existence of these solutions in the space of equation parameters and initial conditions. (C) 2016 Elsevier GmbH. All rights reserved.
Using symbolic computation, we apply the exp-function method to construct new kinds of solutions to the foam drainage equation. We demonstrate that the exp-function method provides a powerful mathematical tool for sol...
详细信息
Using symbolic computation, we apply the exp-function method to construct new kinds of solutions to the foam drainage equation. We demonstrate that the exp-function method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. (C) 2008 Elsevier Ltd. All rights reserved.
Purpose - The purpose of this paper is to use He's exp-functionmethod (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation. Design/methodology/approach - This technique is straigh...
详细信息
Purpose - The purpose of this paper is to use He's exp-functionmethod (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation. Design/methodology/approach - This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems. Findings - This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations. Originality/value - The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh-Nagumo equation illustrates its effectiveness.
In their recent manuscript Lei Zhao et al. claim that they have constructed an algorithm for automatic construction of solitary wave solutions to nonlinear partial differential equations based on the exp-function meth...
详细信息
In their recent manuscript Lei Zhao et al. claim that they have constructed an algorithm for automatic construction of solitary wave solutions to nonlinear partial differential equations based on the exp-function method. We argue that this algorithm does inherit all problems associated to the exp-function method. We show that this algorithm produces solutions which do not satisfy the original differential equation. Even if the solutions would be correct, the exp-function method would not be able to determine necessary and sufficient conditions for the existence of solitary solutions in the space of initial conditions and parameters. (C) 2014 Elsevier Inc. All rights reserved.
By using symbolic computation, we apply the exp-function method to construct new kinds of solutions of (2 + 1)-dimensional variable coefficient Broer-Kaup system. We show that the exp-function method provides a powerf...
详细信息
By using symbolic computation, we apply the exp-function method to construct new kinds of solutions of (2 + 1)-dimensional variable coefficient Broer-Kaup system. We show that the exp-function method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. (C) 2009 Elsevier Ltd. All rights reserved.
One of the advantages of the variational iteration method is the free choice of initial guesses. In this paper we use the basic idea of the exp-function method to construct a generalized trial function with some unkno...
详细信息
One of the advantages of the variational iteration method is the free choice of initial guesses. In this paper we use the basic idea of the exp-function method to construct a generalized trial function with some unknown parameters. The Klein-Gordon equation is used to illustrate the effectiveness and convenience of the method, some new explicit travelling wave solutions are obtained which include bell-type soliton solution, kink-type soliton solution, and generality solitary wave solutions. (C) 2009 Published by Elsevier Ltd
The aim of present paper is to obtain the analytical solution of Harry Dym equation by using exp-functionmethod (EFM). He’s exp-functionmethod is used to construct solitary and soliton solutions of nonlinear evolut...
详细信息
In this Letter we use the exp-function method for analytic treatment for the modified Benjamin-Bona-Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically ...
详细信息
In this Letter we use the exp-function method for analytic treatment for the modified Benjamin-Bona-Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically change the characteristics of the equations, is examined. It is shown that the exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics. (C) 2007 Elsevier B.V. All rights reserved.
In this paper, we implemented the exp-function method and the extended tanh method to finds the analytical solutions of one of the important nonlinear partial differential equations with variable coefficients called t...
详细信息
In this paper, we implemented the exp-function method and the extended tanh method to finds the analytical solutions of one of the important nonlinear partial differential equations with variable coefficients called the new (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients. Moreover, we find the numerical solutions to that equation using the finite difference method. The results demonstrate the effectiveness and convenience of the used methods. Comparison between our results through some tables and graphs to illustrate the accuracy of the applied methods. We obtained the different types of solutions-like bright, dark, periodic, rational and singular periodic soliton solutions using the different values of constant parameters. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients model. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
exp-function and other standard functionmethods for solving nonlinear differential equations are generalized in this paper. An analytical criterion determining if a solution can be expressed in a form comprising stan...
详细信息
exp-function and other standard functionmethods for solving nonlinear differential equations are generalized in this paper. An analytical criterion determining if a solution can be expressed in a form comprising standard functions is derived. New computational algorithm for automatic identification of the structure of the solution is constructed. The algorithm provides information if the solution can be expressed as a sum of standard functions, a ratio of sums of standard functions, or even a more complex algebraic form involving standard functions. Several examples are used to illustrate the proposed concept. (C) 2010 Elsevier Inc. All rights reserved.
暂无评论