Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions

2012 ◽  
Vol 29 (6) ◽  
pp. 060203 ◽  
Author(s):  
Yong-Qi Wu
Keyword(s):  
Exact Solutions ◽  
Lattice Equation

SU(N) LIE ALGEBRA, EXTENDED TODA LATTICE EQUATION AND THE EXACT SOLUTIONS

1994 ◽  
Vol 09 (06) ◽  
pp. 525-534
Author(s):  
A. ROY CHOWDHURY ◽  
A. GHOSE CHOUDHURY
Keyword(s):  
Exact Solutions ◽  
Lie Algebra ◽  
Toda Lattice ◽  
Two Dimensional ◽  
Lattice Equation ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Dimensional Gravity ◽  
Differential Generalization ◽  
Toda Lattice Equation

An integro-differential generalization of the Toda lattice equation is proposed via the zero curvature equation belonging to SU(N) Lie algebra. It is shown that the exact solutions for this equation can be constructed by the method of chiral vectors. Explicit results are given for SU(2) and SU(3). We also demonstrate that these equations are connected to the constrained WZW theory and hence Polyakov’s two-dimensional gravity.

Darboux transformation and exact solutions for a three-field lattice equation

2010 ◽  
Author(s):  
Hai-qiong Zhao ◽  
Zuo-nong Zhu ◽  
Wen Xiu Ma ◽  
Xing-biao Hu ◽  
Qingping Liu
Keyword(s):  
Exact Solutions ◽  
Darboux Transformation ◽  
Lattice Equation

Kink-Type Solutions of the MKdV Lattice Equation with an Arbitrary Function

2014 ◽  
Vol 989-994 ◽  
pp. 1716-1719 ◽  
Author(s):  
Sheng Zhang ◽  
Ying Ying Zhou ◽  
Bin Cai
Keyword(s):  
Exact Solutions ◽  
Difference Equations ◽  
Arbitrary Function ◽  
Function Method ◽  
Variable Coefficients ◽  
Spatial Structures ◽  
Improved Method ◽  
Lattice Equation

In this paper, the exp-function method is improved for constructing exact solutions of nonlinear differential-difference equations with variable coefficients. To illustrate the validity and advantages of the improved method, the mKdV lattice equation with an arbitrary function is considered. As a result, kink-type solutions are obtained which possess rich spatial structures. It is shown that the improved exp-function method can be applied to some other nonlinear differential-difference equations with variable coefficients.

Extension of the Homotopy Perturbation Method for Solving Nonlinear Differential-Difference Equations

2010 ◽  
Vol 65 (12) ◽  
pp. 1060-1064 ◽  
Author(s):  
Mohamed Medhat Mousa ◽  
Aidarkan Kaltayev ◽  
Hasan Bulut
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Difference Equations ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Lattice Equation ◽  
Convenient Tool ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
De Vries

In this paper, we have extended the homotopy perturbation method (HPM) to find approximate analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Korteweg-de Vries (mKdV) lattice equation and the discretized nonlinear Schr¨odinger equation are taken as examples to demonstrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons are made between the results of the presented method and exact solutions. The obtained results reveal that the HPM is a very effective and convenient tool for solving such kind of equations.

scholarly journals Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Khaled A. Gepreel ◽  
A. R. Shehata
Keyword(s):  
Exact Solutions ◽  
Difference Equations ◽  
Elliptic Functions ◽  
Mathematical Physics ◽  
Jacobi Elliptic Function ◽  
Lattice Equation ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Saturable Nonlinearity ◽  
New Exact Solutions ◽  
Elliptic Solutions

We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

scholarly journals Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Qianqian Yang ◽  
Qiulan Zhao ◽  
Xinyue Li
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Spectral Problem ◽  
Darboux Transformation ◽  
Hamiltonian Structure ◽  
Explicit Solutions ◽  
Liouville Integrability ◽  
Lattice Equation ◽  
Integrable Lattice ◽  
Matrix Spectral Problem

An integrable lattice hierarchy is derived on the basis of a new matrix spectral problem. Then, some properties of this hierarchy are shown, such as the Liouville integrability, the bi-Hamiltonian structure, and infinitely many conservation laws. After that, the Darboux transformation of the first integrable lattice equation in this hierarchy is constructed. Eventually, the explicitly exact solutions of the integrable lattice equation are investigated via graphs.

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