scholarly journals Constructing exact solutions to differential-difference equations via the coupled Riccati equations

2008 ◽  
Vol 57 (6) ◽  
pp. 3305
Author(s):  
Yang Xian-Lin ◽  
Tang Jia-Shi
Keyword(s):  
Exact Solutions ◽  
Difference Equations ◽  
Riccati Equations ◽  
Coupled Riccati Equations

A novel iterative algorithm for solving coupled Riccati equations

2020 ◽  
Vol 364 ◽  
pp. 124645 ◽  
Author(s):  
Ai-Guo Wu ◽  
Hui-Jie Sun ◽  
Ying Zhang
Keyword(s):  
Iterative Algorithm ◽  
Riccati Equations ◽  
Coupled Riccati Equations

Exact Solutions for Fractional Differential-Difference Equations by (G'/G)-Expansion Method with Modified Riemann-Liouville Derivative

2016 ◽  
Vol 8 (2) ◽  
pp. 293-305 ◽  
Author(s):  
Ahmet Bekir ◽  
Ozkan Guner ◽  
Burcu Ayhan ◽  
Adem C. Cevikel
Keyword(s):  
Difference Equation ◽  
Exact Solutions ◽  
Difference Equations ◽  
Applied Mathematics ◽  
Expansion Method ◽  
New Exact Solutions ◽  
Liouville Derivative ◽  
Nonlinear Lattice ◽  
Fractional Differential ◽  
Differential Difference Equation

AbstractIn this paper, the (G'/G)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential difference equation into its differential difference equation of integer order. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.

scholarly journals Solitons and Other Exact Solutions for Two Nonlinear PDEs in Mathematical Physics Using the Generalized Projective Riccati Equations Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
A. M. Shahoot ◽  
K. A. E. Alurrfi ◽  
I. M. Hassan ◽  
A. M. Almsri
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Riccati Equations ◽  
Mathematical Physics ◽  
Nonlinear Pdes ◽  
Nls Equation ◽  
The Given ◽  
Order Dispersion

We apply the generalized projective Riccati equations method with the aid of Maple software to construct many new soliton and periodic solutions with parameters for two higher-order nonlinear partial differential equations (PDEs), namely, the nonlinear Schrödinger (NLS) equation with fourth-order dispersion and dual power law nonlinearity and the nonlinear quantum Zakharov-Kuznetsov (QZK) equation. The obtained exact solutions include kink and antikink solitons, bell (bright) and antibell (dark) solitary wave solutions, and periodic solutions. The given nonlinear PDEs have been derived and can be reduced to nonlinear ordinary differential equations (ODEs) using a simple transformation. A comparison of our new results with the well-known results is made. Also, we drew some graphs of the exact solutions using Maple. The given method in this article is straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physics.

Oscillatory Second Order Linear Difference Equations and Riccati Equations

1987 ◽  
Vol 18 (1) ◽  
pp. 54-63 ◽  
Author(s):  
John W. Hooker ◽  
Man Kam Kwong ◽  
William T. Patula
Keyword(s):  
Difference Equations ◽  
Riccati Equations ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Linear
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