Abstract. TOPEX/POSEIDON (T/P) sea level deviation (SLD) time series from 3 October 1992 to 15 May 1997 combined with upper ocean thermal structures are used to observe the characteristics and analyze the dynamics of equatorial waves in the Pacific Ocean. The evolution of the Kelvin wave propagating along an eastward shoaling thermocline in the equatorial Pacific is investigated. The behaviour of this wave as it propagates eastward can be approximately described with the solutions of the perturbed Korteweg-de Vries (PKDV) equation and modified Green's Law. Assuming that the nonlinear term and dispersive term of this equation are balanced, the amplitude increases as the thermocline decreases to the power -3/8. Approaching the eastern Pacific, the nonlinearity increases and the relation changes to the power -9/8. The dispersion relation, and mass and energy conservations are investigated. The results indicate that under a varying thermocline, the nonlinear Kelvin solitary waves indeed exist in the real ocean.