Using the classical Lie theorem on realizations of Lie algebras by vector fields on the line, we substantially simplify the proof of the known results on group classification of the class of (1+1)-dimensional nonlinear evolution equations \(u_t=H(u_{xx})\) .

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On Group Classification of Nonlinear Heat Equation: Algebraic Approach

  • Sofiia Huraka,
  • Oleksandra Lokaziuk

摘要

Using the classical Lie theorem on realizations of Lie algebras by vector fields on the line, we substantially simplify the proof of the known results on group classification of the class of (1+1)-dimensional nonlinear evolution equations \(u_t=H(u_{xx})\) .