Infinitely Many Conservation Laws of a Differential-difference Equation and Backlund Transformation

Chinese Quarterly Journal of Mathematics ›› 2007, Vol. 22 ›› Issue (2): 312-316.

Department of System Science and Mathematic Zhengzhou University,Department of System Science and Mathematic Zhengzhou University,,Zhengzhou 450000 China ,Zhengzhou 450000 China

Received:2006-04-30 Online:2007-06-30 Published:2023-11-07
About author:YANG Xiao(1980-),female,native of Xinyang,Henan,Ph.D.,engages in PDE;WANG Jun- min(1972-),male,native of Ruzhou,Henan,Ph.D.,engagee in aoliton and integrable ayatem.
Supported by:
Supported by the NSF of Henan Prevince(062110300)；

Abstract

Abstract: In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given for- mularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.

Key words: conservation law, Lax representation, Backlund transformation

CLC Number:

O175.7

YANG Xiao, WANG Jun-min. Infinitely Many Conservation Laws of a Differential-difference Equation and Backlund Transformation[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(2): 312-316.

[1]	WANG Jun-jie, LI Sheng-ping. Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation [J]. Chinese Quarterly Journal of Mathematics, 2017, 32(2): 172-180.
[2]	WEI Han-yu, CUI Zhong-yuan, XIA Tie-cheng. Self-consistent Sources and Conservation Laws for Super-Geng Equation Hierarchy [J]. Chinese Quarterly Journal of Mathematics, 2016, 31(2): 201-210.
[3]	WANG Li-juan. Large-time Behavior of Solutions for Parabolic Conservation Laws with Large Initial Data [J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 232-237.
[4]	WU Yong-qi. The Backlund Transformation and Explicit Solution of Volterra Lattice Equation [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(1): 81-85.
[5]	LIU Fa-gui, ZHANG Yuan-zhang . Quasilinear Hyperbolic Conservation Laws with Relaxation [J]. Chinese Quarterly Journal of Mathematics, 2007, 22(1): 143-154.
[6]	ZHANG Ling-yuan, ZHANG Jin-liang, WANG Ming-liang. Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients [J]. Chinese Quarterly Journal of Mathematics, 2006, 21(4): 522-528.

Infinitely Many Conservation Laws of a Differential-difference Equation and Backlund Transformation

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 6

Recommended Articles

Metrics

Comments