scholarly journals Darboux transform and conservation laws of new differential-difference equations

2020 ◽  
Vol 24 (4) ◽  
pp. 2519-2527
Author(s):  
Sheng Zhang ◽  
Dongdong Liu
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Spectral Problem ◽  
Difference Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Darboux Transforms

Darboux transforms, exact solutions and conservation laws are important topics in thermal science and other fields as well. In this paper, the new non-linear differential-difference equations associated a discrete linear spectral problem are studied analytically. Firstly, the Darboux transform of the studied equations is constructed, and exact solutions are then obtained. Finally, infinite many conservation laws are derived.

scholarly journals Infinite many conservation laws of discrete system associated with a 3×3 matrix spectral problem

2017 ◽  
Vol 21 (4) ◽  
pp. 1613-1619
Author(s):  
Sheng Zhang ◽  
Dongdong Liu
Keyword(s):  
Conservation Laws ◽  
Spectral Problem ◽  
Difference Equations ◽  
Discrete System ◽  
Nanoporous Materials ◽  
Electron Conduction ◽  
Alternative Approach ◽  
Non Linear ◽  
Linear Differential ◽  
Matrix Spectral Problem

Differential-difference equations are often considered as an alternative approach to describing some phenomena arising in heat/electron conduction and flow in carbon nanotubes and nanoporous materials. Infinite many conservation laws play important role in discussing the integrability of non-linear differential equations. In this paper, infinite many conservation laws of the non-linear differential-difference equations associated with a 3?3 matrix spectral problem are obtained.

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

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