Compatibility, Multi-brackets and Integrability of Systems of PDEs

被引:0
|
作者
Boris Kruglikov
Valentin Lychagin
机构
[1] University of Tromsø,Institute of Mathematics and Statistics
来源
Acta Applicandae Mathematicae | 2010年 / 109卷
关键词
Multi-brackets; Jacobi-Mayer bracket; Spencer cohomology; Koszul homology; Buchsbaum-Rim complex; Integral; Characteristics; System of PDEs; Symbols; Compatibility; 35N10; 58A20; 58H10; 35A30;
D O I
暂无
中图分类号
学科分类号
摘要
We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi-Mayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of generalized complete intersections and evaluate the formal functional dimension of the solutions space. The results are used to establish new integration methods.
引用
收藏
页码:151 / 196
页数:45
相关论文
共 50 条
  • [1] Compatibility, Multi-brackets and Integrability of Systems of PDEs
    Kruglikov, Boris
    Lychagin, Valentin
    ACTA APPLICANDAE MATHEMATICAE, 2010, 109 (01) : 151 - 196
  • [2] Compatibility, multi-brackets and integrability of systems of PDEs
    Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway
    Acta Appl Math, 1600, 1 (151-196):
  • [3] Multi-brackets of differential operators and compatibility of PDE systems
    Kruglikov, B
    Lychagin, V
    COMPTES RENDUS MATHEMATIQUE, 2006, 342 (08) : 557 - 561
  • [4] Integrability of Lie brackets
    Crainic, M
    Fernandes, RL
    ANNALS OF MATHEMATICS, 2003, 157 (02) : 575 - 620
  • [5] Integrability of Poisson brackets
    Crainic, M
    Fernandes, RL
    JOURNAL OF DIFFERENTIAL GEOMETRY, 2004, 66 (01) : 71 - 137
  • [6] Stability of class II correction with the Austro Repositioner associated with multi-brackets fixed appliances in dolichofacial patients
    María Dolores Austro-Martinez
    Ana I. Nicolás-Silvente
    Mª Angeles Requena
    Marta Carazo-Austro
    José Antonio Alarcón
    BMC Oral Health, 24
  • [7] Higher Haantjes Brackets and Integrability
    Piergiulio Tempesta
    Giorgio Tondo
    Communications in Mathematical Physics, 2022, 389 : 1647 - 1671
  • [8] Higher Haantjes Brackets and Integrability
    Tempesta, Piergiulio
    Tondo, Giorgio
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2022, 389 (03) : 1647 - 1671
  • [9] Stability of class II correction with the Austro Repositioner associated with multi-brackets fixed appliances in dolichofacial patients
    Austro-Martinez, Maria Dolores
    Nicolas-Silvente, Ana I.
    Requena, Ma Angeles
    Carazo-Austro, Marta
    Alarcon, Jose Antonio
    BMC ORAL HEALTH, 2024, 24 (01)
  • [10] Mayer brackets and solvability of PDEs - I
    Kruglikov, B
    Lychagin, V
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2002, 17 (2-3) : 251 - 272