Integrability aspects of the vortex filament equation for pseudo-null curves

被引：5

作者：

del Amor, Jose ^{[1
]}

Gimenez, Angel ^{[2
]}

Lucas, Pascual ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat, Campus Espinardo, E-30100 Murcia, Spain

[2] Univ Miguel Hernandez Elche, Ctr Invest Operat, Avda Univ S-N, Elche 03202, Alicante, Spain

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2017年 / 14卷 / 06期

关键词：

Curve evolution; pseudo-null curves; Lie algebra; integrability; Burgers' equation; EVOLUTION; SURFACES; SYSTEMS; MOTIONS;

D O I：

10.1142/S0219887817500906

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An algebraic background in order to study the integrability properties of pseudo-null curve motions in a three-dimensional Lorentzian space form is developed. As an application, we delve into the relationship between the Burgers' equation and the pseudo-null vortex filament equation. A recursion operator for the pseudo-null vortex filament equation is also provided.

引用

页数：21

共 28 条

[1] [Anonymous], 1993, DIRAC STRUCTURES INT
[2] [Anonymous], 1991, What is Integrability?
[3] Integrable systems in three-dimensional Riemannian geometry
Beffa, GM
Sanders, JA
Wang, JP
[J]. JOURNAL OF NONLINEAR SCIENCE, 2002, 12 (02) : 143 - 167
[4] Blaszak M., 1998, Multi-Hamiltonian Theory of Dynamical Systems
[5] Burgers JM, 1948, Advances in Applied Mechanics, V1, P171
[6] Integrable equations arising from motions of plane curves. II
Chou, KS
Qu, CZ
[J]. JOURNAL OF NONLINEAR SCIENCE, 2003, 13 (05) : 487 - 517
[7] Motions of curves in similarity geometries and Burgers-mKdV hierarchies
Chou, KS
Qu, CZ
[J]. CHAOS SOLITONS & FRACTALS, 2004, 19 (01) : 47 - 53
[8] Del Amor J., 2016, ADV MATH PHYS, V2016, P1
[9] A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms
del Amor, Jose
Gimenez, Angel
Lucas, Pascual
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2015, 88 : 94 - 104
[10] Hamiltonian structure for null curve evolution
del Amor, Jose
Gimenez, Angel
Lucas, Pascual
[J]. NONLINEARITY, 2014, 27 (11) : 2627 - 2641

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