In this paper we discuss the problem of a nonlinear gravity inertial wave of twodimensions and the possibility of solitary wave’s existence. First of all, the existingcondition and analytic solution expression of shallow water waves are obtained by theapplication of the qualitative method of O. D. Es. We find that when the problem is de-generated, some physical values produce the nonlinear solitary wave, while other physi-cal values will be unbounded, so we consider that the nonlinear solitary wave for thesystem does not exist. Then we introduce concepts of the generalized energy (i. e. pseu-do-energy): when the pseudo-energy produces the tiny change at acting on a special ex-ternal effect, there will be solitary waves in this system. Finally, we obtain the repre-sentative of the nonlinear solitary wave which is different from KdV equation.
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