Computation of densities and fluxes of nonlinear differential-difference equations

被引：22
作者：
Hickman, MS
Hereman, WA
机构：
[1] Univ Canterbury, Dept Math & Stat, Christchurch 1, New Zealand
[2] Colorado Sch Mines, Dept Math & Comp Sci, Golden, CO 80401 USA
来源：
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2003年 / 459卷 / 2039期
关键词：
conserved densities; DDEs; semi-discrete lattices; lattice; nonlinear chains; Miura map;
D O I：
10.1098/rspa.2003.1151
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
Direct methods to find conserved densities and fluxes of differential-difference equations are presented and illustrated for the Kac-van Moerbeke (KvM) and modified Volterra lattices. A Miura map which connects both lattices is explicitly constructed based on homotopic deformation. The map is used recursively to compute conserved densities of the KvM lattice. The algorithms presented could be implemented in computer algebra systems and could be used to investigate the integrability of semi-discrete lattices.
引用
收藏
页码：2705 / 2729
页数：25
相关论文
共 47 条
[1]   Multi-component Volterra acid Toda type integrable equations [J].
Adler, VE ;
Svinolupov, SI ;
Yamilov, RI .
PHYSICS LETTERS A, 1999, 254 (1-2) :24-36
[2]   Symmetry approach to the integrability problem [J].
Adler, VÉ ;
Shabat, AB ;
Yamilov, RI .
THEORETICAL AND MATHEMATICAL PHYSICS, 2000, 125 (03) :1603-1661
[3]  
CHERDANTSEV I, 1996, CRM P LECT NOTES, V9, P51
[4]   MASTER SYMMETRIES FOR DIFFERENTIAL-DIFFERENCE EQUATIONS OF THE VOLTERRA TYPE [J].
CHERDANTSEV, IY ;
YAMILOV, RI .
PHYSICA D, 1995, 87 (1-4) :140-144
[5]  
CLARKSON PA, 1999, LONDON MATH SOC LECT, V255
[6]  
FERMI E, 1965, COLLECTED WORKS ENRI, V2, P978
[7]   Symbolic computation of conserved densities for systems of nonlinear evolution equations [J].
Goktas, U ;
Hereman, W .
JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (05) :591-621
[8]   Computation of conserved densities for systems of nonlinear differential-difference equations [J].
Goktas, U ;
Hereman, W ;
Erdmann, G .
PHYSICS LETTERS A, 1997, 236 (1-2) :30-38
[9]   Computation of conservation laws for nonlinear lattices [J].
Göktas, U ;
Hereman, W .
PHYSICA D, 1998, 123 (1-4) :425-436
[10]   Algorithmic computation of generalized symmetries of nonlinear evolution and lattice equations [J].
Göktas, Ü ;
Hereman, W .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1999, 11 (01) :55-80
12345