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Lie symmetries of inviscid Burgers’ equation. (English) Zbl 1173.35699
Summary: The present paper solves completely the problem of the Lie group analysis of nonlinear equation $$u_{t}(x,t) + g(u)u_{x}(x, t) = 0$$, where $$g(u)$$ is a smooth function of $$u$$. And apply these results on inviscid Burgers equation.

##### MSC:
 35Q58 Other completely integrable PDE (MSC2000) 35Q35 PDEs in connection with fluid mechanics 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
##### Keywords:
Lie group analysis; Burgers equation; symmetry group
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