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.
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