Infinitely Many Local Higher Symmetries without Recursion Operator or Master Symmetry: Integrability of the Foursov-Burgers System Revisited

被引：2

作者：

Sergyeyev, Artur ^{[1
]}

机构：

[1] Silesian Univ Opava, Math Inst, Opava 74601, Czech Republic

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 109卷 / 01期

关键词：

Higher symmetries; Recursion relation; Recursion operator; Master symmetry; C-integrability; Linearization; EVOLUTION-EQUATIONS; CONSERVATION-LAWS; NONLOCAL SYMMETRIES; PDES;

D O I：

10.1007/s10440-009-9452-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Burgers-type system studied by Foursov, w(t) = w(xx) + 8ww(x) + (2 - 4 alpha)zz(x), z(t) = (1 - 2 alpha)z(xx) - 4 alpha zw(x) + (4 - 8 alpha)wz(x) - (4 + 8 alpha)w(2)z + (-2 + 4 alpha)z(3), for which no recursion operator or master symmetry was known so far, and prove that this system admits infinitely many local higher symmetries that are constructed using a nonlocal two-term recursion relation rather than a recursion operator.

引用

页码：273 / 281

页数：9

共 36 条

[1]

[Anonymous], 1993, DIRAC STRUCTURES INT

[2]

[Anonymous], 1991, What is Integrability

[3] On integrability of systems of evolution equations [J].

Beukers, F ;

Sanders, JA ;

Wang, JP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 172 (02) :396-408

[4]

Blaszak M., 1998, Multi-Hamiltonian Theory of Dynamical Systems

[5]

Bocharov AV, 1999, Symmetries and Conservation Laws for Differential Equations of Mathematical Physics

[6] THE HIERARCHY OF THE BENJAMIN-ONO-EQUATION [J].

FOKAS, AS ;

FUCHSSTEINER, B .

PHYSICS LETTERS A, 1981, 86 (6-7) :341-345

[7] GENERALIZED CONDITIONAL SYMMETRIES AND EXACT-SOLUTIONS OF NONINTEGRABLE EQUATIONS [J].

FOKAS, AS ;

LIU, QM .

THEORETICAL AND MATHEMATICAL PHYSICS, 1994, 99 (02) :571-582

[8] Conservation laws of evolution equations: Generic non-existence [J].

Foltinek, K .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 235 (01) :356-379

[9] On integrable coupled Burgers-type equations [J].

Foursov, MV .

PHYSICS LETTERS A, 2000, 272 (1-2) :57-64

[10] RECURSION OPERATORS AND NONLOCAL SYMMETRIES [J].

GUTHRIE, GA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1994, 446 (1926) :107-114

← 1 2 3 4 →