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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm8549https://doi.org/10.4213/mzm8549 https://www.mathnet.ru/eng/mzm/v87/i1/p122
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