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Lie symmetries of the equation $u_{t}(x, t) + g(u)u_{x}(x, t) = 0$. (English) Zbl 1129.35003
The authors use the basic prolongation method and the infinitesimal criterion of invariance to find some particular Lie point symmetries group of the nonlinear equation $\frac{\partial}{\partial t}u(x,t)+g(u)\frac{\partial}{\partial t}u(x,t)=0$ with a smooth function $g(u)$. For the case of inviscid Burger’s equation, where $g(u)=u(x,t)$, the Lie projectable symmetry algebra is determined and its connections with some other differential equations are found. Moreover it is shown how these symmetries may be used to construct some exact solutions of these equations.
35A30Geometric theory for PDE, characteristics, transformations
35Q53KdV-like (Korteweg-de Vries) equations
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