Supplement to “Self-similar solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in ” [Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 4524–4528]

Based on the characteristic method, we construct a new class of perturbational solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in R N . Such solutions are more general than those obtained by Yuen [Yuen MW. Self-similar solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in R N . Commun Nonlinear Sci Numer Simul 17 2012; 4524–8.]. The perturbational solutions may have applications in explaining the drifting phenomena of the propagation wave like Tsunamis in oceans when N = 2 .