Now showing items 1-10 of 20
Similarity solutions to Burgers' equation in terms of special functions of mathematical physics
(Jagellonian University, 2017-07)
In this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is ...
Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions
In this paper we present a numerical solution method for the Bernoulli free boundary value problem for the Laplace equation in three dimensions. We extend a nonlinear integral equation approach for the free boundary ...
Multi-wave and rational solutions for nonlinear evolution equations
(De Gruyter, 2010-08)
Nonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.
Application of the Exp-function method to the (2+1)-dimensional Boiti-Leon-Pempinelli equation using symbolic computation
(Taylor & Francis, 2011-03)
Locate full-text(opens in a new window)|Full Text(opens in a new window)|View at Publisher| Export | Download | Add to List | More... International Journal of Computer Mathematics Volume 88, Issue 4, March 2011, ...
Construction of exact solutions for fractional-type difference-differential equations via symbolic computation
This paper deals with fractional-type difference-differential equations by means of the extended simplest equation method. First, an equation related to the discrete KdV equation is considered. Second, a system related to ...
Q-Shock soliton evolution
By generating function based on Jackson's q-exponential function and the standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to q-Hermite polynomials with ...
Comment on: "Application of Exp-function method for (3+1 )-dimensional nonlinear evolution equations" [Comput. Math. Appl. 56 (2008) 14511456]
We show that Boz and Bekir [A. Boz, A. Bekir, Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations, Comput. Math. Appl. 56 (2008) 14511456] obtained some incorrect solutions for the equations ...
Travelling wave solutions to nonlinear physical models by means of the first integral method
(Indian Academy of Sciences, 2011-04)
This paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical ...
Exact and explicit solutions to nonlinear evolution equations using the division theorem
In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a ...
The first integral method for constructing exact and explicit solutions to nonlinear evolution equations
Problems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some ...