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Titlebook: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics; W. I. Fushchich,W. M. Shtelen,N. I. Serov Book 1993

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书目名称Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics
编辑W. I. Fushchich,W. M. Shtelen,N. I. Serov
视频video
丛书名称Mathematics and Its Applications
图书封面Titlebook: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics;  W. I. Fushchich,W. M. Shtelen,N. I. Serov Book 1993
描述by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors‘ works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi­ sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork­ ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.
出版日期Book 1993
关键词Theoretical physics; algebra; calculus; differential equation; mathematical physics; operator; partial dif
版次1
doihttps://doi.org/10.1007/978-94-017-3198-0
isbn_softcover978-90-481-4244-6
isbn_ebook978-94-017-3198-0
copyrightSpringer Science+Business Media Dordrecht 1993
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Mathematics and Its Applicationshttp://image.papertrans.cn/t/image/883952.jpg
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https://doi.org/10.1007/978-94-017-3198-0Theoretical physics; algebra; calculus; differential equation; mathematical physics; operator; partial dif
发表于 2025-3-22 05:36:07 | 显示全部楼层
Euclid and Galilei Groups and Nonlinear PDEs for Scalar Fields,In the present chapter we describe a wide class of nonlinear PDEs for scalar fields invariant under Euclid, Galilei, or larger groups. For some of such equations we construct multiparameter families of exact solutions.
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Poincare-Invariant Nonlinear Scalar Equations,al and tangent symmetry of the relativistic Hamilton equation, of the nonlinear d’Alembert equation, of the Euler-Lagrange-Born-Infeld equation, the Monge-Ampere equation, and some other PDEs. For this purpose the Lie method has been used with the exception of Sec. 1.3, where the symmetry of the pol
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Systems of PDEs Invariant Under Galilei Group,ations (such as the extended Galilei group, the Schrödinger group). Sets of Sch(1,3)- and G(1,3)-nonequivalent ansatze are constructed. A wide class of linear and nonlinear Sch(1,3)-invariant systems of PDEs is described. Lame equations are studied: superalgebra of symmetry is found and a Galilei-in
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Poincare-Invariant Nonlinear Scalar Equations,onge-Ampere equation, and some other PDEs. For this purpose the Lie method has been used with the exception of Sec. 1.3, where the symmetry of the polywave equation is investigated by the operator method expounded in Sec. 5.5.
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