Abstract: By using a perturbation method, a forced mKdV equation is derived from the so-called quasi-geostrophic vorticity equation, and time evolutions of mass and energy of the mKdV solitary waves are discussed. Finally, numerical solutions of the forced mKdV equation are obtained by using the pseudo-spectral method. The calculation results show that the features of the mKdV solitary waves excited by localized external source are closely related to the detuning parameter α and the strength of the external source. The external forcing source in a forced mKdV system can excite larger amplitude and more instable disturbances than those in a forced KdV system.

Key words: forced mKdV equation, external source, solitary wave