Symmetries of Integro-Differential Equations: A Survey of Methods Illustrated by the Benny Equations

被引:0
作者
N. H. Ibragimov
V. F. Kovalev
V. V. Pustovalov
机构
[1] Blekinge Institute of Technology,International Research Centre ALGA: Advances in Lie Group Analysis, Department of Mathematics, IHN
[2] Russian Academy of Sciences,Institute for Mathematical Modelling
来源
Nonlinear Dynamics | 2002年 / 28卷
关键词
integro-differential equation; symmetry; Benny equations;
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学科分类号
摘要
Classical Lie group theory provides a universal tool for calculatingsymmetry groups for systems of differential equations. However Lie'smethod is not as much effective in the case of integral orintegro-differential equations as well as in the case of infinitesystems of differential equations.
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页码:135 / 153
页数:18
相关论文
共 33 条
  • [1] Benny D. J.(1973)Some properties of long nonlinear waves Studies in Applied Mathematics L11 45-50
  • [2] Kupershmidt B. A.(1977)Long-wave equation with free boundary. I. Conservation laws and solutions Functional Analysis and Its Applications 11 188-197
  • [3] Manin Y. I.(1978)Long-wave equation with free boundary. II. Hamiltonian structure and higher equations Functional Analysis and Its Applications 12 20-29
  • [4] Kupershmidt B. A.(1980)Benny equation and quasiclassical approximation in the method of the inverse problem Functional Analysis and Its Applications 14 89-98
  • [5] Manin Y. I.(1981)Collisionless Boltzmann equations and integrable moment equations Physica D 3 503-511
  • [6] Zakharov V. E.(1976)On the symmetry of one-dimensional high-frequency motions of a collisionless plasma Journal of Technical Physics 46 1271-1277
  • [7] Gibbons J.(1982)Group invariant solutions of kinetic equations Mechanics of Fluids and Gazes 4 135-140
  • [8] Taranov V. B.(1983)On some invariant transformations of kinetic equations Vestnik, Moscow State University, Series 1, Mathematics-Mechanics 4 69-72
  • [9] Bunimovich A. I.(1995)A method for computing symmetries and conservation laws of integro-differential equations Acta Applicandae Mathematicae 41 45-56
  • [10] Krasnoslobodtsev A. V.(1995)Modeling integro-differential equations and a method for computing their symmetries and conservation laws American Mathematical Society Translations 167 1-22