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In this paper, beginning with the shallow-water equations describing the geophysical fluid motion and by a method expanding the nonlinear terms in Taylor series near the equilibrium point, we find the analytic solutions of the finite amplitude nonlinear inertio-surface gravity waves and Rossby waves. We point out that (ⅰ) the finite amplitude nonlinear inertio-surface gravity waves and Rossby waves Satisfy all the KdV equations; (ⅱ) the solutions are all the enoidal functions, i. e. the enoidal waves which include the linear waves and form the solitary waves under certain conditions; (ⅲ) the dispersive relation including both the wave number and the amplitude is established; (ⅳ) the rotating transform method is given, and the two-dimensional nonlinear problem can be reduced to the one-dimensional one.
In this paper, beginning with the shallow-water equations describing the geophysical fluid motion and by a method expanding the nonlinear terms in Taylor series near the equilibrium point, we find the analytic solutions of the finite amplitude nonlinear inertio-surface gravity waves and Rossby waves We point out that (i) the finite amplitude nonlinear inertio-surface gravity waves and Rossby waves Satisfy all the KdV equations; (ii) the solutions are all the enoidal waves, ie the enoidal waves which include the linear waves and form the solitary waves under certain conditions; (iii) the dispersive relation including both the wave number and the amplitude is established; (ⅳ) the rotating transform method is given, and the two-dimensional nonlinear problem can be reduced to the one-one one.