关键词: mKdV方程, 强迫, 耗散

Abstract: By using a perturbation method, a forced mKdV-Burgers equation is derived from the geostrophic potential vorticity equation including dissipation and topography. An approximate analytic solution of the mKdV-Burgers equation is obtained for the case with a small dissipation. The time evolution of mass and energy of the solitary waves is analyzed, and finally the numerical solutions of the forced mKdV-Burgers equation with a small dissipation are given for a localized topographic forcing by using the pseudo-spectral method. The numerical results show that the presence of small dissipation causes a slow decrease of the amplitude and the propagation speed of the solitary waves and slow increase of the solitary wave width. In the nonlinear system with dissipation and topographic forcing, the dissipation factor forces a moving solitary wave to oscillate in the forcing region during the interaction between the solitary wave and the topographic forcing, and it is advantageous to form large amplitude disturbances.

Key words: mKdV equation, forcing, dissipation