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Classification of similarity solutions for inviscid Burgers’ equation. (English) Zbl 1188.35010
Summary: Using the basic Lie symmetry method, we find the most general Lie point symmetries group of the inviscid Burgers’ equation. Looking at the adjoint representation of the obtained symmetry group on its Lie algebra, we find the preliminary classification of its group-invariant solutions. The latter provides new exact solutions for the inviscid Burgers’ equation.
MSC:
35B06Symmetries, invariants, etc. (PDE)
35C05Solutions of PDE in closed form
35K58Semilinear parabolic equations
58J70Invariance and symmetry properties