Now showing items 1-10 of 43
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 ...
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.
Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the (3 + 1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and ...
Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method
We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. ...
The Ablowitz-Ladik lattice system by means of the extended (G′ / G)-expansion method
We analyzed the Ablowitz-Ladik lattice system by using the extended (G′ / G)-expansion method. Further discrete soliton and periodic wave solutions with more arbitrary parameters are obtained. We observed that some previously ...
A note on the (G′/G)-expansion method again
We report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved.
Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G′/G)-expansion method
In this paper, we demonstrate the effectiveness of the so-called (G′/G)-expansion method by examining some nonlinear evolution equations with physical interest. Our work is motivated by the fact that the (G′/G)-expansion ...
Application of the G′ / G-expansion method to Kawahara type equations using symbolic computation
In this paper, Kawahara type equations are selected to illustrate the effectiveness and simplicity of the G′ / G-expansion method. With the aid of a symbolic computation system, three types of more general traveling wave ...
Analytic investigation of the (2 + 1)-dimensional Schwarzian Korteweg–de Vries equation for traveling wave solutions
(Elsevier BV., 2011-02-15)
By means of the two distinct methods, the Exp-function method and the extended (G0/G)-expansion method, we successfully performed an analytic study on the (2 + 1)-dimensional Schwarzian Korteweg–de Vries equation. We ...
The discrete (G′/G)-expansion method applied to the differential-difference Burgers equation and the relativistic Toda lattice system
We introduce the discrete (G′/G)-expansion method for solving nonlinear differential-difference equations (NDDEs). As illustrative examples, we consider the differential-difference Burgers equation and the relativistic ...