The Prasad-Sommerfield-like, colorless anl finite-mass dyon anolytic solution in SU(5) grond unified model is found. It is the only physical dyon solution so far.
The analytical solutions for the stead state equations of four wave mixing with an arbitrary complex coupling constant are given without the undepleted pump approximation.
This homotopic method is an approximate analysis method, which can be more used for analyzing other behavior of the sea surface temperature anomaly of the atmosphere-ocean oscillator model.