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

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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. 
@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},
     publisher = {mathdoc},
     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a12/}
}
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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/