LOCAL GEOMETRIC INVARIANTS OF INTEGRABLE EVOLUTION-EQUATIONS

被引：27

作者：

LANGER, J ^{[1
]}

PERLINE, R ^{[1
]}

机构：

[1] DREXEL UNIV, DEPT MATH & COMP SCI, PHILADELPHIA, PA 19104 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1994年 / 35卷 / 04期

关键词：

D O I：

10.1063/1.530567

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.

引用

页码：1732 / 1737

页数：6

共 37 条

[1]

BACKLUND AV, 1882, MATH ANN, V19, P387

[2]

Batchelor G. K., 1967, INTRO FLUID DYNAMICS

[3]

CHAU LL, 1984, 13TH P INT C GROUP T

[4] EXACT SOLUTION TO LOCALIZED-INDUCTION-APPROXIMATION EQUATION MODELING SMOKE RING MOTION [J].

CIESLINSKI, J ;

GRAGERT, PKH ;

SYM, A .

PHYSICAL REVIEW LETTERS, 1986, 57 (13) :1507-1510

[5]

Eisenhart L., 1909, TREATISE DIFFERENTIA

[6] N-SOLITONS ON A CURVED VORTEX FILAMENT [J].

FUKUMOTO, Y ;

MIYAZAKI, T .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1986, 55 (12) :4152-4155

[7] METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION [J].

GARDNER, CS ;

GREENE, JM ;

KRUSKAL, MD ;

MIURA, RM .

PHYSICAL REVIEW LETTERS, 1967, 19 (19) :1095-&

[8] SOLITONS, EULER EQUATION, AND VORTEX PATCH DYNAMICS [J].

GOLDSTEIN, RE ;

PETRICH, DM .

PHYSICAL REVIEW LETTERS, 1992, 69 (04) :555-558

[9] THE KORTEWEG-DEVRIES HIERARCHY AS DYNAMICS OF CLOSED CURVES IN THE PLANE [J].

GOLDSTEIN, RE ;

PETRICH, DM .

PHYSICAL REVIEW LETTERS, 1991, 67 (23) :3203-3206

[10] NONLINEAR MODULATION OF GRAVITY-WAVES [J].

HASIMOTO, H ;

ONO, H .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1972, 33 (03) :805-&

← 1 2 3 4 →