Loop algebra of Lie symmetries for a short-wave equation
This paper deals with symmetry transformations of the nonlinear differential equation \[ 2\cdot K\cdot \Phi_ x+\Phi_{yy}+2\cdot \Phi_{xt}-2\cdot (x+\Phi_ x)\cdot \Phi_{xx}=0 \] of short waves. The Lie algebra of symmetries is discussed and characterized in connection to the loop or Virasoro algebra, its structure is given by a tensor product of a finite-dimensional part and the space \(L(t,t^{-1})\) of Laurent polynomials. Using the adjoint representation to form special generators, solutions generated by the corresponding transformations are constructed.
scientific article; zbMATH DE number 4058495