The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables

被引：1

作者：

Froehlich, Sara ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, 805 Sherbrooke St West, Montreal, PQ H3A 0B9, Canada

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

Laplace transform; conservation laws; Darboux integrable; variational bi-complex; hyperbolic second-order equations; C-SPECTRAL SEQUENCE; CONSERVATION-LAWS; DIFFERENTIAL-EQUATIONS; CHARACTERISTIC COHOMOLOGY; LAPLACE TRANSFORMATIONS; LAGRANGIAN-FORMALISM; DIMENSIONS; DARBOUX;

D O I：

10.3842/SIGMA.2018.096

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I. M., Kamran N., Duke Math. J. 87 (1997), 265-319]. The constrained variational bi-complex is introduced and used to de fine form-valued conservation laws. A method for generating conservation laws from solutions to the adjoint of the linearized system associated to a system of PDEs is given. Finally, Darboux integrability for a system of three equations is discussed and a method for generating in finitely many conservation laws for such systems is described.

引用

页数：49

共 36 条

[1]

ANDERSON I, 1992, MEM AM MATH SOC, V98, P1

[2]

Anderson I., 1989, The Variational Bicomplex

[3]

Anderson I. M., 1992, Contemp. Math., V132, P51, DOI [10.1090/conm/132/1188434, DOI 10.1090/CONM/132/1188434]

[4] Superposition formulas for exterior differential systems [J].

Anderson, Ian M. ;

Fels, Mark E. ;

Vassiliou, Peter J. .

ADVANCES IN MATHEMATICS, 2009, 221 (06) :1910-1963

[5] The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane [J].

Anderson, IM ;

Kamran, N .

DUKE MATHEMATICAL JOURNAL, 1997, 87 (02) :265-319

[6]

[Anonymous], CBMS REGIONAL C SERI

[7]

[Anonymous], 1995, Selecta Math. (N.S.), V1, P265, DOI 10.1007/BF01671567

[8]

Bryant R., 1995, SEL MATH, V1, P21, DOI [10.1007/BF01614073, DOI 10.1007/BF01614073]

[9] CHARACTERISTIC COHOMOLOGY OF DIFFERENTIAL-SYSTEMS .2. CONSERVATION-LAWS FOR A CLASS OF PARABOLIC EQUATIONS [J].

BRYANT, RL ;

GRIFFITHS, PA .

DUKE MATHEMATICAL JOURNAL, 1995, 78 (03) :531-676

[10] CHARACTERISTIC COHOMOLOGY OF DIFFERENTIAL-SYSTEMS .1. GENERAL-THEORY [J].

BRYANT, RL ;

GRIFFITHS, PA .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 8 (03) :507-596

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