Articles written in Pramana – Journal of Physics
Volume 74 Issue 2 February 2010 pp 207-218 Research Articles
The ($G'/G$)-expansion method for a discrete nonlinear Schrödinger equation
Sheng Zhang Ling Dong Jin-Mei Ba Ying-Na Sun
An improved algorithm is devised for using the ($G'/G$)-expansion method to solve nonlinear differential-difference equations. With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with parameters are obtained, from which some special solutions including the known solitary wave solution are derived by setting the parameters as appropriate values. It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics.
Volume 76 Issue 4 April 2011 pp 561-571
A transformed rational function method for (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation
A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial differential equations.
Volume 81 Issue 5 November 2013 pp 763-773 Research Articles
A generalized exp-function method for multiwave solutions of sine-Gordon equation
Sheng Zhang Jian Wang Au-Xue Peng Bin Cai
In this paper, the exp-function method is generalized to sine-Gordon (s
Volume 85 Issue 6 December 2015 pp 1143-1156
Variable-coefficient nonisospectral Toda lattice hierarchy and its exact solutions
In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the compatibility condition of Toda spectral problem and its time evolution. In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and more general exact solutions are obtained. It is shown that the inverse scattering transformation can be generalized to solve some other nonisospectral lattice hierarchies with variable coefficients.
Volume 97, 2023
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