Variable coefficient KdV equation and the analytical diagnoses of a dipole blocking life cycle

A variable coefficient Korteweg de Vries (VCKdV) system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a dipole blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data is well described by the analytical solution.