Geodesic
On the Symmetry Classification and Conservation Laws for Quasilinear Differential Equations of Second Order
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 122-129

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : tangent transformation, Lie group, Euler–Poisson equation, Laplace transform. 
Yu. A. Chirkunov. On the Symmetry Classification and Conservation Laws for Quasilinear Differential Equations of Second Order. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 122-129. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a12/
@article{MZM_2010_87_1_a12,
     author = {Yu. A. Chirkunov},
     title = {On the {Symmetry} {Classification} and {Conservation} {Laws} for {Quasilinear} {Differential} {Equations} of {Second} {Order}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {122--129},
     year = {2010},
     volume = {87},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a12/}
}
TY  - JOUR
AU  - Yu. A. Chirkunov
TI  - On the Symmetry Classification and Conservation Laws for Quasilinear Differential Equations of Second Order
JO  - Matematičeskie zametki
PY  - 2010
SP  - 122
EP  - 129
VL  - 87
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a12/
LA  - ru
ID  - MZM_2010_87_1_a12
ER  - 
%0 Journal Article
%A Yu. A. Chirkunov
%T On the Symmetry Classification and Conservation Laws for Quasilinear Differential Equations of Second Order
%J Matematičeskie zametki
%D 2010
%P 122-129
%V 87
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a12/
%G ru
%F MZM_2010_87_1_a12

[1] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[2] L. V. Ovsyannikov, “Gruppovye svoistva uravneniya S. A. Chaplygina”, PMTF, 1960, no. 3, 126–145