Abstract
On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations
Highlights
Many physical, biological and chemical phenomena can be modeled using partial differential equations (PDEs) and differential-difference equations (DDEs)
In the last decades, many researchers have been interested in obtaining exact solutions of PDEs and DDEs
Our objective in this paper is to investigate the equivalence between the Backlund transformation of Riccati equation method (BTREM) and the extended tanh-function method (ETM)
Summary
Biological and chemical phenomena can be modeled using partial differential equations (PDEs) and differential-difference equations (DDEs). Many methods were proposed for achieving this task Some of these methods are: the tanh method [1], the extended tanh-function method (ETM) [2], the simplest equation method [3], the integral bifurcation method [4], the extended mapping transformation method [5,6] and the Backlund transformation of Riccati equation method (BTREM) [7–12]. I=0 where ai, i = 0, 1, 2, , n are some constants that will be computed later, n is a positive integer computed by the balance between the highest-order derivative term and the nonlinear terms in the Equation (3) and φ satisfies the following Riccati equation:. The Riccati Equation (5) has the following solutions: 1. To zero, we get a set of algebraic equations for ai, i = 0, 1, 2, ..., n Solving this obtained system will lead to the values of ai, i = 0, 1, 2, ..., n
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