Symmetry algebra of the Benjamin-Ono equation
This paper concerns the Benjamin-Ono equation in the form \[ u_t=2uu_x+Hu_{xx}, \] where \(H\) is the Hilbert transform operator \[ Hu(x)= {1\over\pi} P\int^{+\infty}_{-\infty} {u(z)\over x-z} dz. \] Here \(P\) denotes the principal value. The Lie algebra structure for symmetries of the Benjamin-Ono equation is completely described.
scientific article; zbMATH DE number 1340259