In the present work ¯rst order accurate implicit di®erence scheme for
the numerical solution of the nonlinear Charney-Obukhov equation with vari-
able coe±cients is constructed. On the basis of numerical calculations accom-
plished by means of this scheme, the dynamics of two-dimensional nonlinear
solitary vortical structures at the presence of sheared °ow is studied. For the
considered equations the initial-boundary value problem is set when at the ini-
tial moment the solution in the form of di®erent solitary structures are taken.
The problem of stability for the ¯rst order accurate semi-discrete scheme is in-
vestigated. For solving of the considered di®erence scheme iteration method is
o®ered. Convergence of this iteration method is proved. Suggested numerical
method for investigation of dynamics of nonlinear Rossby waves propagation in
the earth's neutral atmosphere under conditions of sheared zonal °ows is used.
Obtained results su±ciently well describe physical picture of phenomena.