On the nonlocal equations and nonlocal charges associated with the Harry Dym hierarchy

被引:18
作者
Brunelli, JC
da Costa, GATF
机构
[1] Univ Fed Santa Catarina, CFM, Dept Fis, BR-88040900 Florianopolis, SC, Brazil
[2] Univ Fed Santa Catarina, CFM, Dept Matemat, BR-88040900 Florianopolis, SC, Brazil
关键词
D O I
10.1063/1.1512974
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given. (C) 2002 American Institute of Physics.
引用
收藏
页码:6116 / 6128
页数:13
相关论文
共 24 条
[1]  
ADLER M, 1979, INVENT MATH, V50, P219
[2]   HIERARCHY OF LOWER KORTEWEG-DEVRIES EQUATIONS AND SUPERSYMMETRY STRUCTURE OF MIURA-TRANSFORMATIONS [J].
ANDREEV, VA ;
SHMAKOVA, MV .
JOURNAL OF MATHEMATICAL PHYSICS, 1993, 34 (08) :3491-3506
[3]   R-MATRIX FORMULATION OF KP HIERARCHIES AND THEIR GAUGE EQUIVALENCE [J].
ARATYN, H ;
NISSIMOV, E ;
PACHEVA, S ;
VAYSBURD, I .
PHYSICS LETTERS B, 1992, 294 (02) :167-176
[4]  
CALOGERO F, 1982, SPECTRAL TRANSFORM S, V1
[5]   AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].
CAMASSA, R ;
HOLM, DD .
PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664
[6]   SOLITON STRUCTURE VERSUS SINGULARITY ANALYSIS - 3RD-ORDER COMPLETELY INTEGRABLE NONLINEAR DIFFERENTIAL-EQUATIONS IN 1+1-DIMENSIONS [J].
FUCHSSTEINER, B ;
CARILLO, S .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1989, 154 (03) :467-510
[7]  
Gesztesy F., 1992, REP MATH PHYS, V31, P113, DOI DOI 10.1016/0034-4877(92)90008-O
[8]   DERIVATION AND IMPLICIT SOLUTION OF THE DYM,HARRY, EQUATION AND ITS CONNECTIONS WITH THE KORTEWEG-DEVRIES EQUATION [J].
HEREMAN, W ;
BANERJEE, PP ;
CHATTERJEE, MR .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (03) :241-255
[9]   On a completely integrable nonlinear hyperbolic variational equation [J].
Hunter, J.K. ;
Zheng, Y. .
Physica D: Nonlinear Phenomena, 1994, 79 (2-4)
[10]   AN R-MATRIX APPROACH TO NONSTANDARD CLASSES OF INTEGRABLE EQUATIONS [J].
KONOPELCHENKO, B ;
OEVEL, W .
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1993, 29 (04) :581-666