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Matematicheskie Zametki, 2010, Volume 87, Issue 1, Pages 122–129
DOI: https://doi.org/10.4213/mzm8549
(Mi mzm8549)
 

This article is cited in 3 scientific papers (total in 3 papers)

On the Symmetry Classification and Conservation Laws for Quasilinear Differential Equations of Second Order

Yu. A. Chirkunov

Novosibirsk State University for Economics and Management
Full-text PDF (447 kB) Citations (3)
References:
Abstract: We obtain a sufficient condition for the absence of tangent transformations admitted by quasilinear differential equations of second order and a sufficient condition for the linear autonomy of the operators of the Lie group of transformations admitted by weakly nonlinear differential equations of second order. We prove a theorem concerning the structure of conservation laws of first order for weakly nonlinear differential equations of second order. We carry out the classification by first-order conservation laws for linear differential equations of second order with two independent variables.
Keywords: quasilinear (weakly nonlinear) differential equation of second order, conservation laws for differential equations, tangent transformation, Lie group, Euler–Poisson equation, Laplace transform.
Received: 07.06.2008
Revised: 02.06.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 1, Pages 115–121
DOI: https://doi.org/10.1134/S0001434610010141
Bibliographic databases:
UDC: 517.944+519.46
Language: Russian
Citation: Yu. A. Chirkunov, “On the Symmetry Classification and Conservation Laws for Quasilinear Differential Equations of Second Order”, Mat. Zametki, 87:1 (2010), 122–129; Math. Notes, 87:1 (2010), 115–121
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm8549
  • https://doi.org/10.4213/mzm8549
  • https://www.mathnet.ru/eng/mzm/v87/i1/p122
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    Abstract page:550
    Full-text PDF :220
    References:64
    First page:27
     
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